It's mildly irritating, but I wouldn't restart for that. If you try to stick to forests and hills it's rare to lose a unit to animals.
Naval auto-explore never seems to get anywhere.
You should be able to stay out of a bears way for the most part, if you stick to forests chances are you'll win the fight with a warrior and with a scout a bear should never catch you.
if you step your warrior wrong all of a sudden bam.. it's gay.
I never lose Settlers or Workers to Bears or Lions. Move one space, and if you see a Lion or Bear, move back. If you don't see one, hit the space bar. That's right, leave a movement point. Otherwise, you might stop right next to an animal. And then lunch is on! This technique doesn't help with Wolves or Panthers.