Cell has an original personality, with various other characters' personality traits added in; Gero's computer redesigned the weak aspects of the original personality, adding in the personalities of various different characters to make him the perfect weapon. Throughout the Androids Arc, Cell's personality changes drastically with each transformation. At first, Cell's desire to complete his evolution by absorbing both Android 17 and Android 18 is what fuels him in his imperfect form. Upon reaching his final form, his eagerness to test the limits of his newfound power is what defines his character. Cell is unique among most villains of the series in that he is quite sophisticated. Because of his genetic composition from other warriors, he is able to psychologically manipulate those warriors and exploit their weaknesses to his advantage. He also found the Dragon Balls' reviving ability to be a nuisance, as evidenced by his relief when he learned that the Dragon Balls were rendered inert due to Piccolo and Kami's fusion.
Initially, Cell is completely single-minded in the pursuit of his goals and is very cautious, sneaky, cunning, knowledgeable, and calculating in achieving his main goal of perfection. Upon reaching his first transformation, he becomes far more brash and impulsive in his actions, relying less on strategy and more on brute force, often becoming clouded and losing his ability to think rationally when things don't go his way. However, he does retain at least some degree of a strategic mind, as he got the idea to exploit Vegeta's arrogant desire for a challenge to manipulate him into allowing him to absorb 18. Upon reaching perfection, Cell displays a number of traits shared by those whose cells he possesses; Piccolo's cunning, Vegeta's pride, Goku's laid-back disposition, Frieza's smugness (as well as some of his psychopathy), and the Saiyan lust for battle. He is also shown to be very calm and genuinely polite in this Perfect form. Perhaps Cell's most distinguishable trait in this form is his uninhibited vanity, which he shamelessly puts on display by launching the Cell Games, a tournament organized for the sole purpose of showing off his newfound power. It can also be seen during Cell's confrontation with Gohan when he affirms his true purpose: the annihilation of anything he considers imperfect, a category in which he places everyone and everything but himself. But when he is outmatched he quickly becomes desperate and makes mistakes. Ironically, the arrogant trait Vegeta displayed to allow Cell to achieve his perfect form was the same trait Cell used to force Gohan to awaken his hidden powers, which led to his own downfall, almost directly emulating Vegeta.
In the English manga, Cell is referred to as "it", while in the anime (and the Japanese versions of both), he is referred to as "he." He is likely described that way in the English manga to emphasize the fact that he is an artificial being (though the English manga does occasionally refer to him as "he").
As Imperfect Cell, Cell is completely single-minded in the pursuit of his goals to complete his evolution, as he is extremely eager to discover what attaining perfection would feel like. His desire is to absorb both Android 17 and Android 18. Imperfect Cell is very cautious, sneaky, cunning, and calculating; he does not chase after the Androids directly since he knows he cannot beat them before he absorbs enough human energy. Although obsessed with attaining perfection, Cell was willing to temporarily put aside his plans to absorb 17 and 18 if it meant that he had to deal any possible threat to his plans, as seen how he chose to dispatch Piccolo and attempted to do so with 16 rather than immediately going after 17 and 18.
However, despite his usually cautious and savvy nature, Imperfect Cell could still be seen to be somewhat arrogant and narcissistic, seen by how he openly revealed his plans to Piccolo when under the impression that he had won.
After he achieves his Semi-Perfect form, Cell no longer cares about absorbing other creatures, and becomes obsessed with finding Android 18 to complete his quest for perfection. He also becomes slightly more arrogant and narcissistic because of his power increase, as well as rash and impatient. His arrogance is short-lived though; he is easily outclassed by Vegeta's Super Saiyan Second Grade form. After finding that his Semi-Perfect form is no match for his opponent, Cell convinces Vegeta to allow him to absorb Android 18 to attain the Perfect Form (which he is able to do as he appeals to Vegeta's ego and the natural Saiyan drive to fight stronger opponents, both of which Cell is aware of, as he possesses Vegeta's cells). He is also prone to tantrums when things don't go his way. This is best evidenced when he was unable to find Android 18 and proceeded to blow up several islands in an attempt to force her to come out, not caring if his energy blasts resulted in her destruction if she tried to continue hunker down.
According to his bios in Dragon Ball Z: Budokai Tenkaichi 2 and Budokai Tenkaichi 3, in his new form, he seems to feel that he is the most powerful living specimen on the planet, and it is suggested that this arrogant attitude may have been influenced by Vegeta's genes (meaning Vegeta's cells may become more prominent while in this form, which seems to be supported by the fact he uses at least two of Vegeta's signature moves in this form, albeit only in the anime: Galick Gun and a modified Big Bang Attack). It may also be due to his absorption of Android 17 and the genes of Frieza, both of whom are very egotistical, arrogant, narcissistic, and intolerant of the idea of anyone being better than themselves. To further support the notion of his superiority, Android 16, who barely survives his brief encounter with this form of Cell, thinks to himself that there should be no one in the universe ready to challenge him at this point (and that it is odd how he is still so obsessed with achieving completion), until this preconception is shattered by Cell's embarrassment against the self-proclaimed "Super Vegeta".
After absorbing No. 18 and becoming perfect, Cell becomes significantly more arrogant and narcissistic in this form, due to the massive increase in power. After attaining the perfect form he had long desired, Cell admitted to Trunks that he had found himself with no other purpose, even killing Goku, which was Dr. Gero's intended purpose for Cell, did not seem to satisfy him. Thus, he saw his Cell Games as the opportunity to discover a new purpose; to test his new-found power. This could also be attributed by his own vanity.
In this form, Cell gains Frieza's polite mannerisms (though without the snide sarcasm) and ruthlessly sadistic personality, relishing in seeing people terrified, as he admitted to Future Trunks when he revealed his intention for the Cell Games. This was further shown in the anime, while waiting for the Cell Games, he chose to terrorize the people of Earth simply for his own amusement. Akira Toriyama himself surmised that the concept behind the Cell Games may have been influenced by King Piccolo's cells which makes sense as King Piccolo also enjoyed terrorizing the people of Earth in a similar manner and both broadcasted their evil intentions on television just to instill fear into Earth's population. Thus he possesses the villainous traits from King Piccolo, Vegeta, and Frieza.
Much like Goku, Cell seems to take on a carefree and laid-back attitude, not losing any form of his composure until he was faced with the prospect of a being stronger than him. Cell has adopted Goku's, as well as Vegeta's, desire to battle strong opponents, which was another purpose of the Cell Games. The fact that prior to facing Super Saiyan 2 Gohan, Cell still chose to hold back his full power, Cell was willing to handicap himself in order to challenge his own limits. Despite this, however, if Cell finds that his opponents were not adequate challenges, he would not hesitate to finish the battle quickly or discontinue it, reflecting his arrogance. Before fighting Gohan, Cell saw Goku as the only worthy opponent and displayed excitement when fighting him. Cell even expressed discontent and outrage when Goku had decided to forfeit his battle against Cell.
After coming back in his Super Perfect form, the huge influx of power causes his already inflated ego to increase dramatically. He becomes notably more deranged, frequently shouting and exhibiting bizarre facial ticks at random intervals (although this may be largely due to his rage over being humiliated by Gohan). In addition, the intro narration for Cell Returns has the narrator referring to Cell as a "demented demon". Cell also became more hotheaded and rash, seen by how he immediately chose to risk destroying the entire solar system simply to defeat Gohan.
After returning from his brush with death, Cell saw himself as true perfection, believing himself to be immortal, as he was unable to die (save for the unlikely possibility of dying in battle). Oddly, despite having every intention of destroying the planet, he was heard thinking "That's the spirit" when Gohan's challenges Cell to a Kamehameha duel (although this was likely because he wanted the latter to give it his all as a means to prove Cell's own superiority). Even as he was slowly destroyed by Gohan's final attack, Cell could not comprehend why he was defeated, exclaiming that he was perfection itself. When in the throes of defeat, Cell seems to almost lose his sanity. Screaming in rage and confusion as he believes no one can defeat "perfection" (or himself). These traits show that Cell most likely has inherited some of Frieza's mental illness and insanity (also matching his psychotic and sadistic traits).
In Dragon Ball Xenoverse 2, Perfect Cell is shown to retain his fondness for absorbing people, though he reason for doing so is not to increase his power but for his own enjoyment. To alleviate his boredom he offers to train the Future Warrior, though threatens he will absorb them should they fail or refuse. While training the Future Warrior, Cell is impressed by the Warrior's growth and even finds that he enjoys teaching and training others, to the point he even suggests he might take on more students. Presumably this trait may come from Piccolo and/or Goku. If the Future Warrior manages to bond fully with both Cell and Frieza a special event occurs where Cell encounters 1st form Frieza for the first time. Though he and Frieza are allies in the anime filler and Dragon Ball GT, during this meeting in Xenoverse 2 Cell is shown to look down on Frieza during this meeting as he contributes his loss during the Cell Games to Frieza's Cells due to Frieza's loss to the Saiyans (Goku and Future Trunks), showing that Perfect Cell seems to blame his faults on others who's DNA he possesses such as Frieza. In return Frieza is show to dislike Cell's smug and arrogant attitude towards him which ironically is a trait that comes from Frieza himself.
However, when Imperfect Cell fights Frieza in the Xenoverse 2 there is a special dialog where Frieza is intrigued by Cell and asks who he is. Cell states that he guesses he should thank him for "supplying" his DNA, even calling it an act of generosity in the Funimation dub of Xenoverse 2.
If Perfect Cell fights with Cell Junior it will act disrespectfully towards him angering Cell causing him to state "How dare you! How dare you act that way towards your father...! You are nothing but a miserable failure." showing that he does not like being disrespected by his children. In Xenoverse 2 when fighting Android 13, Imperfect Cell suspects that Android 13 may be one of his early prototypes as he notes his ability to grow stronger through absorbing the components of other Androids. Perfect Cell (in both his Perfect and Super Perfect forms) however considers Android 13 to be an outdated model.
In Dragon Ball FighterZ, after he is revived Cell is determined to prove himself superior to Android 21, a newer model Bio-Android created from the human mother of Dr. Gero's son & Android 16's human template that incorporates the cells of countless warriors including Cell himself and Majin Buu as well as countless scientists and researchers. However in both the Super Warrior Arc and Android 21 Arc, he is shown to be inferior to Android 21 and is absorbed by Android 21 in the first arc while absorbed by Android 21 (Evil) in the final arc. In the Enemy Warrior Arc, he joins forces with the revived Frieza Force (Frieza, Nappa, Saibamen, Ginyu Force, and an unseen Sorbet). He and Frieza later declare a temporary truce with the Z Fighters in order to combat Android 21 and her army of clones, as the power suppressing waves prevent them from utilizing their power unless soul linked. When they are confronted by Android 16, he suggests Krillin join Android 16 when he is reluctant to fight him, though Krillin refuses to side with the Red Ribbon Army before noting Cell was created by them. Cell however states that while Dr. Gero did create him he has no loyalty to it, causing Krillin to admit his disgust at Cell for not having any sense of loyalty or obligation, though hopes that Android 16 surrenders before he is killed as he reluctantly finds himself fighting alongside Cell. This fits with Cell perfectionism and self centeredness as he refuses to be controlled by the army that created him (as Android 21 is considered the de facto leader of the Red Ribbon Army and was responsible for Cell's revival and attempted to control him by linking him with an artificial soul but Cell bent it to his will in all three arcs).
Cell's refusal to serve the army whose destruction was responsible for his creation is likely due to the influence of Vegeta and Frieza's cells as both refuse to be controlled (unless faced with someone they fear and know they cannot defeat like Beerus) and dislike taking orders from others. Cell is also not surprised that Android 21 cloned a perfect being like himself though he considers his clones to be inferior as he believes it is impossible to clone perfection, though their mindlessness likely contributions to this as they lack his personality thus are noting but inferior copies in his eyes. While he is willing to begrudgingly work the Z Fighters in the Enemy Warrior Arc and the human soul in the Super Warrior Arc, he maintains his arrogance and perfectionism, as well as his desire to get revenge on Gohan and Goku, though is disappointed by Gohan's strength due to his lack of training. He also notes that he can't sense Super Saiyan Blue Vegeta's ki though correctly surmises it is a form of Super Saiyan that is stronger than a regular Super Saiyan, though he is not intimidated by it as he is excited at the chance to test his strength against SSGSS Vegeta (however this is mainly due to his Saiyan genes, belief in his own superiority, and inability to sense how strong SSGSS Vegeta actually is due to being unable to sense godly ki). It is implied that he suffered the same punishment in Earth's Hell as Frieza and like Frieza was traumatized by it, though in Cell's case he refuses to elaborate on the so-called "horrors" he witnessed. Though Frieza dislikes certain aspects of his personality (presumably because Cell's perfectionist attitude reminds Frieza of his elder brother, as Frieza notes that is what he despises about Cooler in Xenoverse 2), the two get along due to their shared hatred of the Z Fighters and Android 21, even remaining allies once they ended their truce with the Z Fighters after Android 21's defeat (Frieza is known to put aside his differences with Cooler when they share a common enemy, so it is not surprising that the same thing would happen with Cell). However in other arcs, Frieza and Cell's alliance is less stable and they are defeated as a result. Due to being unable to sense godly ki and ignorant of more powerful entities outside of the main story, Cell remains ignorantly confident of his power and abilities when confronting characters such as Beerus, Super Saiyan 3 Gotenks, Vegito Blue, Super Saiyan Rosé Goku Black, and Fused Zamasu though this is mainly due to his delusion that he is perfect along with his desire to test his power. After winning a match teamed with Android 18, he notes he would absorb 17 & 18 if he still had the ability implying that he lost the ability to absorb them after gaining his Super Perfect Form following his regeneration after his self-destruction.