Wow....very tough question....there are so many characters across different genres that I love....
Based on how often I re-read a book or re-watch a movie (after all, I have to come up with SOME criteria!) I would say:
Drizzt D'Urdan from The Dark Elf book series (R.A.Salvatore). My favorite artist's drawing of him is the cover of The Two Swords. I realize the series isn't "serious fantasy", but for a light entertainment read there's nothing like Drizzt to bring a smile to your face! I also like the way he is drawn in the comic book series.
V from V for Vendetta movie
Temeraire from the Termeraire book series by Naomi Novick. (aren't really any artist's renditions of him yet).
Of course, my favorites change with time.
To the poster that said Arya Stark: Hell Yeah! And her brother Rob too! Though I will say I hope that the next book picks up the pace somewhat. I found the last one rather tiresome.
And for those of you who may be surprised that no character from LoTR is on my list: That's because the whole of LoTR IS my all time favorite.