Curious about rabies

Hi,
I was thinking about this last night. Yesterday I found and caught a
stray/feral kitten, which managed to give me a bite (mistaking my thumb for
food rather than out of fear/aggression!) This is not the first time I've
been bitten by a feral. Fortunately in Australia we don't have rabies, so
I've never been too worried about handling stray/feral animals. How does
rabies impact on handling unknown domestic animals in US? What happens if
you get bitten by an animal you don't know? Does this affect the average
animal lover's ability to catch/handle stray animals?

Just wondering...

Thanks,
Purplecat