Terrifying Rescuer: Until Fiona realizes he's actually a much better prospect than the prince.
Villain Protagonist: In the first film, all he wanted to do was kick all the refugees out of the swamp by dealing with Farquaad's demands. Eventually, he grows out of this and ends up becoming The Hero.
Et Tu, Rapunzel?: In Shrek the Third, the betrayal of her and the other Princesses by Rapunzel, who was in love with Prince Charming.
Everything's Better with Princesses: Both subverted and played straight. Notably, Fiona's perfectly willing to live in squalor with the man she loves, but she's got more of a sense for duty and family - and she's a strong feminist woman to boot.
Ambiguously Bi: In the second movie, when he hears the Ugly Stepsister describe how handsome Prince Charming is, he replies with "Mmm. Sounds dreamy."
Anti-Hero: When he first appeared he had no qualms about murdering Shrek for money. However, he shows a clear sense of ethics by joining Shrek in gratitude for saving him and quickly becomes a good guy for the rest of the series.
Running Gag: He always seems to come close to becoming a real boy, only for those plans to fall short, like in Shrek 2, when he does become a boy, only to immediately be turned back by accident, and in Forever After, when he's about to sign a contract to be turned into a real boy, only for the interaction to be interrupted.
Literal Ass Kissing: Unintentionally invoked. She was preparing to kiss Donkey (with the latter being somewhat unwilling). Shrek knocks Donkey off her, only to end up being kissed himself, right on the place that you'd expect. As soon as she found out what happened, she wasn't happy.
Our Dragons Are Different: Initially appears to be your average guardian fire-breather. Turns out she's sapient and much more developed than classic fairytale dragons, although she doesn't speak, and she can interact with society to an extent. Also, has a thing for talking donkeys.
Samus Is a Girl: Donkey didn't realize this till he starts fast talking her. Really improved his survival chances afterward.
Tsundere: Type A in Shrek. Ditched in all following installments.
The Speechless: Expresses herself mostly in grunts. Donkey does enough speaking for both of them.
What Happened to the Mouse?: The ending of Shrek 2 showed six Dronkeys including a red-colored one - named "Eclair" according to merchandise. Though, for some reason she never shows up in the third movie.
Villainous Breakdown: Has one when Shrek storms his wedding and Fiona reveals her nature as an ogress. He orders his knights to seize them both and starts shouting for order and ranting about how he's king.
Black Mail/Cold-Blooded Torture: Subverted only to be played straight later on: When she first appears to Harold, she implies that she is going to torture him when shouting at him for Fiona marrying Shrek. However, it immediately shows that the thing she was gonna do that she didn't want to if he didn't tell her was breaking her diet (apparently, she overindulges on junk food when irritated). Played straight, however, when she threatens Harold with what is heavily implied to be turning him back into a frog if he didn't spike Fiona's tea with a love potion.
Ambiguously Gay: Being voiced by the openly gay Rupert Everett doesn't help. There is a huge Parental Bonus in the scene where he talks to his mother about his reluctance to marry Fiona — apparently, he is not interested in women at all...
He has, however, shown revulsion towards the wolf when he sees him in what is supposed to be Fiona's bed, and it is also implied that he has some reciprocation of romantic feelings for Rapunzel.
Psychopathic Manchild: Hinted at in Shrek 2 (For one thing, when Fairy Godmother is forced to break her diet, he wanted and got a kids meal, shown to be a toy battle axe), and explicitly shown in Shrek the Third.
Overprotective Dad: He loves Fiona, but he doesn't seem to understand her, thinking she'd be better off with Prince Charming than an ogre like Shrek. He comes around at the last minute and accepts that Shrek is right for her.
Pinocchio Syndrome: His apparent backstory. Fairy Godmother turned him from a frog to a human so he could fall in love with his future wife.