I used a plastic flip/humane trap when I lived with my dad.
It could catch up to 5 mice, they walk through the tunnel and get flipped into a holding cell.
I used to take it to work with me when I'd catch one (or more) and let them go in the field behind my work.
I would catch one or more a week.
My dad, using standard neck breaker traps, caught barely anything.
From my experiences, barring a cat, that flip trap (well baited and placed) or glue traps actually work the best. The glue traps are horrible but I have used them in the past.
Someone mentioned skunks before and I've never tried this but I heard the following before and that it works great.
Skunks are nocturnal and usually leave their "home" at night in search of food.
Watch them at night and wait till they ALL leave the nest and are out of view (good and far away).
Sprinkle human hair clippings and urine near where they are comming in/ going out.
Supposedly, when they return home they'll smell your scent and go find another place to live.