I would assume most people aren't happy about being cheated on, especially if they don't know the morphing power exists. If they do know it exists, that just leads to a whole new excuse for people to do horrible things and claim they've been framed by an Animorph. Damn it, now I have a new fanfic idea...
As much as I love the idea of being a hero and fighting crime, I think most people if they were honest would do petty or selfish stuff. I think at best I'd be a minor vigilante rather than an actual hero. Say somebody wrongs me or does something rude, I could easily acquire them and set them up. Or at least sneak into their house and morph snake to scare the crap out of them. I don't think I'd do anything seriously damaging, at least not before I'm inevitably corrupted by power, lol.
Aside from that, I'd do all the usual stuff. Morph a bird to go flying and not have to worry about cost of buses/trains to get around. Morph pets for fun, become a member of the opposite sex just to see what it's like, spy on people to see what they say when I'm not around, morph to heal any injuries I might get, etc.