I have never personally caught a rat or mouse with traps, but I do know others that have used traps to catch rats or mice. I, on the other hand, have used a different means of a trap. A simple plastic cup with peanut butter inside of it. Lay the cup on it's side with peanut butter in it ( the peanut butter keeps the cup in place to prevent it from rolling and it also lures such said mouse or rat into it), wait for the mouse or rat to enter the cup, then take a plastic lid and cover the cup completely. Take the cup outside far enough away from your home and release the mouse or rat. Throw out the cup and lid afterwards.
This way you aren't hurting the rodent or attempting killing it. Yes, rats and mice are a nuisance, but there are other methods, like I mentioned above, to prevent inhumane acts.