Should my cat be allowed to eat the mice he catches?

Question
This past weekend, my cat caught a mouse and after playing with it for about 20-30 minutes, he killed and ate it. It was the first mouse he'd ever eatten. When I mentioned to my mother that my cat had eaten a mouse he'd caught, she told me I should've taken the mouse away from my cat and buried it or thrown it away, that mice have rabies. A friend of mine who has five cats told me that it was probably all right for my cat to eat the mice he catches, but to take my cat to the vet and get him a booster on his rabies vaccine to be on the safe side.  

Should I allow my cat to eat the mice he catches or take them away from him?  The mice he tends to catch are small, proabably baby mice and if I had to guess, their field mice.

Answer
Laura,

Eating mice, while disgusting and disturbing to anyone that isn't a cat is perfectly normal behavior. My worries would certainly be rabies and parasites, and potentially poison. If you are going to allow your cat to eat mice that he catches I would suggest that you make sure that his rabies shot is up to date, and that he is regularly examined for parasites. You should also be aware that by eating field mice your cat does run the risk of being poisoned - the mouse may have left someone's house after having ingested mouse/rat poison.
The only way to prevent your cat from contracting parasites, poisoning or diseases that don't have vaccines is to keep him indoors. He will live a longer and happier, mouse free existance. Hopefully this adequately answers your question. If you have any further questions or concerns please do not hesitate to contact me.