It sounds like slugs or snails --- and one of the best treatments for these critters is to use a slug/snail bait. Look for baits at your local garden center or favorite online retailer; there are traditional and organic types available.
I've also heard that mulching the soil around your plants with coffee grounds can help deter these critters, but I've not tried it myself.
There's an old-time remedy that you can dig a shallow pan of beer in your garden so it's at soil level. A number of slugs/snails will crawl in and drown. This can provide some control, but it's not usually effective in large gardens or if you have a large population of slugs/snails.
---Justin, Senior Garden Editor, BHG.com