I've had the best luck with glue traps and you can often get two with one pad, but get the rat sized pads, not the mouse sized ones. After two or three, they start using their fallen brethren as stepping stones.
The little plastic modernized version of the traditional mouse traps blow. Don't waste money. I only got them because they looked a little safer if I accidentally caught a dog or a cat.
Also, homemade trap, I've caught a lot of suckers at the farm by leaving some dog kibble in the bottom of a five gallon bucket. Downside is that you have to do the killing (or I guess you could return them to the wilds, but I just bop 'em and be done with it)
oh, and then there is always the old standby and get a cat.