When I was thinking about my answer to this question I ended up with two sub-sections - pets I don't like based on how they look and those I don't like based on their abilities. Obviously, some may fit into both categories and these are no doubt pets that will never be battled! I don't think I've found any pets that I dislike (well at least significantly) based on abilities and so I'm going to talk about aesthetics.
Navimie (who thought of the 10 Days of Pet Battling) touched on how pet models look in her answer. She mentions the blocky appearance of the various frogs and I couldn't agree more! They just look terrible.
Aside from the frogs, some other pet models that I really dislike are (images taken from warcraftpets.com):
Marmot / Prairie Dog Model
The marmot / prairie dog model is one of the worst and blockiest models if you ask me!
Chipmunk / Squirrel Model
The chipmunk / squirrel model is again blocky but not the worst - it could just do with a little smoothing over.
Eye of the Legion
Now, the Eye of the Legion is a bit of an odd-ball - I don't dislike it as such but I'm disappointed with it. I'll set the scene - I knew what they looked like but had never seen one as such. I often looked for them on the AH and at WoW TCG Loot but never found a bargain. Then I saw my first one in-game. It happened to be Kaitz' and boy was I disappointed! Theyre soooo small!!! If you haven't seen one imagine that the Arcane Eye and Darkmoon Eye's are footballs (soccer) then the Eye of the Legion is a tennis ball!
I won't rant about Blizz not bothering to update the models as I'm sure they spent/spend their time more wisely but I really hope in the future they work on some of the older pet models. It doesn't bother me if, for example, there's only two different skins (i.e black and white) but the model shape, look etc. really does.