squirrels - I don't swerve, they are quick and small. Its up to them if they make up their mind and move they'll make it, if not, paws up.
cats - never been unlucky with one of those
dogs - hate em. I've only been back to biking for a month or so so I haven't had any run ins but on my motorcycles, I just judge the angle of attack, if they don't have a good angle, twist the wrist and blow past em. If they are smarter and cut me off I go right at the rat bastards, twist the wrist at the last second to lighten the front, they'll pause, I swerve a bit and try to stiff leg kick the crap out of em (I always miss).
Neighbors - worse than squirrels, not quick, more unpredictable
Birds - duck, got hit by one on a motorcycle once. Not pretty.
Deer - pray.

So far since I've been back to biking the only object I've hit is a construction barrel. Darn thing came out of nowhere. Actually I was riding in a pace line eased to the right to take a look ahead and BAM. Fortunately it was laying on its side, I reacted fast and skipped off it back to the left. Scared the crap out of the two riders behind me though.