I noticed something as I've been re-reading the series--by that, I mean the few books I can get my hands on. In Animorphs: The Escape, it is hinted--if not openly stated--that Tobias suffers from a fear of water. He says it has something to do with him being a hawk, but I think it's also implied that he's afraid of not being able to breathe once submerged. We see more of this in the Exposed, when Tobias morphs a Sperm Whale.
We then see that Marco develops a fear of insects--or, at least, morphing insects.
Ax, being an Andalite, is claustrophobic, but also has some issues when it comes to Elfangor and his parents--but that's a whole new can of worms, isn't it?
Now, I'm not sure about the others, since I haven't read nearly enough Animorphs books. I can speculate that Jake fears losing those close to him, or putting those he loves in danger.
Anyone have any ideas?