I feel Like I don't have that many favourite brickfilm characters. Probably mostly due to brickfilms being relatively short thus one can't really develop a liking for the character as easily, with the exception of the LEGO movie, which might count, in which case Benny and Unikitty are my favourites with the wizard and Emmet next.
As far as shorter home-made brickfilms, I'd say Robophelia, one of the reoccurring characters from Nightly News at Nine. I really love how she's not a regular minifigure and does all kinds of wacky stuff with her robot arms to express what she's saying, plus she has that fun jolly personality even in the face of adversity. She's an easy favourite.
After her, I also like these people:
The homeless man from TCOTY
The Strange Villain in a Top-Hat from LGFB's films
Zundar Silverspine, also from NNN
The Robot from Play Nice
The Director from Zombie Genesis
Bob from Character Delevopment
And, of course, BIRDFaCE
If I Were A Minifig wrote:"Jonny-Bob" (ANP's How to Not Rob a Bank)
As far as characters I've made myself go, I feel like Johnnybob is one of the best. I've been considering making a cop comedy with him, though I've also been considering making a cop comedy about Hogcherry from Riigo-Faloo.
My favourite characters I've played in another film would probably be the Ax Man or any vampire.