Being one who is fairly decent at Photoshop, I like avatars which I know display a certain amount of both artistic talent/good eye as well as technical expertise in PhotoShop. This doesn't necessarily mean animation...and I'm pretty tired of the avatars which display a series of pictures (with or without captions) as those aren't very hard to make at all. No...I'm really talking about good use of photos, cleaning up of imperfections in photos, good blending ability of two photos together, good but not overdone use of color/tinting, good or creative cropping, interesting use of brushes and effects like blur or texture, good color coordination between the photos and any captions, etc. Nothing ruins an otherwise good avatar as quickly for me as a garish font or font color on captions.
I also look at entries in terms of what that person has entered before: do they have just one skill that they used over and over and over in every contest they enter? Or do they show evidence of having spent alot of time in Photoshop, experimenting, learning, collecting & using interesting brushes & fonts, etc.
I also like avatars which display clever ideas - not necessarily funny (although they can be funny and I love funny avatars), but clever.
Obviously, the entry must meet the thematic requirements of the contest - for me, that's a given.
And I like original entries - not the people who enter the same avatar over and over in different contests around the board.
And finally, originality and use of one's own work is essential. Once or twice I've seen entries in contests that I saw elsewhere - like in contests on LiveJournal. If I suspect someone is plagerising avatars, I obviously don't vote for them. This has happened only a couple of times and I haven't noticed it recently (maybe because I've not been able to do LJ like I used to). But if I notice a plagerizer, I never vote for them again. PERIOD. As in, ever.