The Evil Prince: Subverted partially, interestingly. While he still is an evil prince, contrary to this trope, he is actually a pious son with immense respect for his father - even if their relationship is cool and strained at best. He wants to rule, but he doesn't mind waiting for his father to kick the bucket naturally - and his one elder brother kindly removed himself from the line of succession by sacrificing himself to save Cao Cao.
Played straight, however, in the fates his other brothers meet after he assumes power. (And it would have been worse, had their mother not interfered and forbidden him to kill his brothers; they were "only" exiled and driven to desperation.)
Just look at what happened to his brothers Cao Zhang, Cao Xiong, and almost eventually Cao Zhi (and his friends), though.
At least little Cao Chong seems seems to have died of natural causes at the young age of 13, although the fact that he was originally meant to be Cao Cao's successor makes this... convenient, too. And as Cao Cao remarks to Cao Pi, "This is my misfortune, but your good fortune."
Ambition Is Evil: Played straight, even if his actual intentions are not that bad - he's still keeping daddy's tradition alive and is the villain of his time, or at least seen as such. His brothers can probably share some tales about this, too - or could, if they had come out of it alive.
Happily Married: One could also say that he and Zhen Ji deserve each other. They certainly don't mind, and are perhaps the most vocal couple about their mutual attraction and admiration.
Aristocrats Are Evil: Subverted only in that he didn't grow up as an aristocrat per se, but as a warlord's son. Daddy was not made a duke until well into Cao Pi's adulthood.
Man In White: His DW6-outfit does that (while DW6 makes Zhen Ji essentially the corresponding Woman In White or even Winter Royal Lady). It's in nice contrast to the usually dark, blue or purple outfits the rest of Wei wears. He even rides a white horse.
Warrior Prince: Granted, it was kind of a given in his time.
The Starscream: As Emperor Xian - married to Cao Pi's sister, btw - sadly has to realise after Cao Cao, loyal to the Han all his life, dies, and his son... strongly suggests the emperor offer him the crown.
Ho Yay: Surprisingly little, considering the canon. Arguably with Samurai Warriors' fellow Deadpan Snarker Ishida Mitsunari in Warriors Orochi.
Ugly Guy Hot Wife: Not exactly ugly, perhaps (by Wei's standards sort of handsome, even), but definitely with an insufferable personality, it seems to be a mystery why Zhen Ji, one of the four great beauties, not only freely and willingly marries him, but absolutely adores him - until one realises that she is just about as much of a ruthless, cold-hearted, arrogant bitch as he is a ruthless, cold-hearted, arrogant bastard.
Sibling Rivalry: Especially his younger brother Cao Zhi, most famous for his skills in poetry and his perpetual drunkenness, has to find out about this the hard way. While almost all of Cao Pi's prominent siblings had far greater talents than him in various fields (Cao Zhang was strong as an ox and an amazing general, Cao Zhi was gifted with incredible literary talent, Cao Chong was a child genius with an intelligence surpassing that of most adults at age 5 or 6), sadly nobody possessed an even remotely comparable ruthlessness and shrewdness. When Cao Pi finally took the throne, it only became worse for all of them.
Big Screwed Up Family: Just in case you haven't noticed yet - this doesn't even cover it.
Offered the Crown: Subverted and played straight at once: He forces Emperor Xian to offer him the crown, then declines three times - before finally accepting it and declaring himself Emperor of Cao Wei.
Deadpan Snarker: All that needs to be said is - well, what he says to Sun Quan when meeting him in battle, "Aren't you one of those southern rubes? Shouldn't you be off frolicking in a river somewhere?"
Unfortunate Name: Not only do many non-Chinese speakers upon reading his name assume that it's pronounced "cow pee" (WRONG, by the way), but even in Chinese, his given name Pi1 is very close to the Chinese word pi4, which means "fart".
Warrior Poet: Just like his father, he wasn't only busy on battlefields, but was talented in poetry, too - unfortunately, his younger brother Zhi was far more talented.
Double Weapon / Bifurcated Weapon / Dual-Wielding: His stupidly implausible sword, which is... basically, two swords stuck together at the hilts. He can take them apart and use them as two separate swords in the middle of battle with absurd ease.
Magnificent Bastard: While not normally in the league of his father, he had his moments in Warriors Orochi.
Stuck In Their Shadow: The entire point of his storyline is freeing himself from his larger-than-life father's shadow.
Sword Over Head: He has a moment of doing this to Sima Yi, after capturing the latter during a failed attempt to rebel - before cutting his ties instead and telling him to go back to work, since he needs him as an ally.
Evil Is Sexy: The entire family, apparently. TV-Tropes summed it up better than I could: "Cao Cao, the most elegant of the Three Kingdoms' rulers, and a perfect example of a Magnificent Bastard. Cao Pi, Cao Cao's son. Handsome, dashing, cruel and ambitious. Zhen Ji, Cao Pi's wife (what IS it with this family?), probably the hottest lady in the Dynasty Warriors series and a hell of a bitch."
Crossover Ship: Warriors Orochi made him and Samurai Warriors' Ishida Mitsunari all but a canon item.
Battle Couple: Him and Zhen Ji. And if their comments to each other in battle are anything to go by... watching the other fight is one hell of a turn on for both of them.
Defrosting Ice Queen: He actually manages to do that to Zhen Ji. As does she, to him.
Pragmatic Villainy: While the Cao are classy villains, you can't deny that they are pragmatists to boot. And no, that's not a good thing for you.
The Cao are also closely related to technically part of the Xiahou-clan. Yes. Daddy Cao Cao is the cousin of that Xiahou Dun, the guy who upon being shot in the eye with an arrow, ripped out both arrow and eye, declared he couldn't throw the essence of his parents away, ATE HIS OWN EYE, and then went and ended the archer. All without otherwise flinching.
Not to forget Xiahou Dun's brother Xiahou Yuan, while less famous still one of Wei's leading generals.
There's also Cao Cao's other cousin, Cao Ren, another highly prominent general.
Then, there is Cao Pi's older half-brother Cao Ang, who was cornered along with Cao Cao - and immediately gave up his horse to allow his father to escape, being killed by the pursuing troops in the end.
Also Cao Pi's brother Cao Zhang, who allegedly wrestled and killed wild animals with his bare hands.
And through another marriage, just like with Lady Bian, we also have former Yuan-wife Zhen Ji - one of China's four great beauties, and one cold bitch, who accompanies her husband Cao Pi on battlefields, and whose bloodthirst occasionally impresses even him; he ends up calling her "frightful" in full approval. In a nutshell - this family is hardcore. We don't call Wei a mafia clan for nothing.
The Mafia: What the Cao clan would be if they lived today. You can't even deny it.
Almighty Mum: You don't mess with Lady Bian, no matter who you are. This lady sent one of her grandson's concubines into exile for making a thoughtless comment on Bian's past as a prostitute, and actually forbade her son from killing his brothers after he had been made Prince of Wei.
Even Bad Men Love Their Mamas: See above. Cao Pi was the kind of person who put people to death for criticising him. His mother criticises him? He gives in.
Like Father Like Son: Yes. Oh yes. More than he would like to admit, but less than everybody who knew his father seems to think.
I Am Not My Father: Cao Pi makes a point of declaring and proving this. His contemporaries have trouble believing that he is anything but an inferior Cao Cao v2.0 living to realise his father's ambitions, however.
Overlord Jr: As the trope suggests. He's THE MAN's son, after all. And quite willing to take the title.
Inadequate Inheritor: What he is in the eyes of many of his father's generals, and also of his enemies. It takes quite a bit to convince them otherwise - but he manages.
It's All About Me: This. This is what it really is all about. And he says so, towards Sima Yi at least, openly.
Son Of A Whore: His mother, Lady Bian, is a former prostitute. You better don't make stupid comments on that. She will have your arse for it.
Tough Love: While it's questionable if there is actually any love at all between his father and him, if there is, it is this. On both sides.
Crowning Moment of Heartwarming: Zhen Ji's ending, when after gaining control of the land, he stands in front of a cheering crowd of soldiers with his wife, and suddenly remarks, quite of nowhere, that everything he has achieved has been done for her. She is surprised, and comments that such sweet words are not like him - to which he explains that he thought it would be nice to speak his heart for once. The scene ends with her standing closer to him, and them both looking at their cheering soldiers. If you know the characters, this came out absolutely unexpected and sweet.