There are several types commonly seen in home freshwater aquaria, and many of which will make their way into your tank simply from purchasing plants. After a few purchases I ended up with all 3.

Common pond snail: Really don't know how to describe it except that its features are pretty common (go figure) and really don't stick out from anything else.

Ramshorn snail: Essentially the same as the pond snail, just the shell resembles a ram's horn when looked at from the side.

Malaysian trumpet snail: These guys are noctournal and spend most of daylight (lamp-light) burrowing through the substrate. They have a very hard shell that has a long cone shape with a twirling design resmembling something you might see on an ocean beach.

All of the aforementioned are asexual so only one snail has the propensity to reproduce mass populations within a matter of weeks. This isn't the case for mystery/apple snails. Sometimes they will hitch hike on plants or you may even get plants with snail eggs on them. Their level of reproduction depends mostly upon how much excess food and dissolved organics are in the aquaria. If you overfeed your fish, you may notice the snail population explode rather quickly. I never have a problem with this.

Personally I believe them to aid in plant growth as they're constanly going over the leaves and surfaces of the tank cleaning off things that may prevent some photosynthesis. Some new aquarists view them as pests because they overfeed their fish leading to tons and tons of snails, and even further think they're eating their plants when all they're doing is eating decaying flora--- which is actually all any of the above mentioned snails will eat. They will not harm your plants.

Here's a cool video of malaysian trumpet snails annihilating some patches of algae on a tank.

http://www.youtube.com/watch?v=YDX1j1z5mME