get rid of it! they spawn like mad!!! chances are you have another 10 smaller ones in there. If you dont mind them, but want to keep them in control buy a few clown loaches - they love them!
there are positives to them - they can help clean the tank
all in all i just find them to be pests!
Pretty much the worst advice you can possibly give someone off the top of your head without taking numerous specifics first!
A single Clown Loach is potentially a 12" fish, these fish are one prone to stunted growth if kept in a tank too small - and this is cruel. These are big fish as my grand-father had a 9" one in his 6ft a few years ago. Albeit they are amazing snail eaters, i had a shoal of 5 that loved munching on snail infestations, but to keep 5 of these you would need atleast a 5ft tank IMHO. Some would say that is to small still.
To the OP. There are other alternatives to get rid of these pest snails if you do not like them. To answer your question they do breed on their own, and at an alarming rate. Matt is right in saying you probably already have a zillion minute babies 'snailing' around undetected. So if you want rid of them, you have a few options.
1) Manual removal. Timely, but can prove relatively effective over a period of time. Unfortunately doesnt remove them 100%, or is highly unlikely too.
2) Chemical treatments to kill snails. However, these may prove to be harmfull to shrimp - so ALWAYS read the label on these products.
3) Cucummber slices weighted down during lights out. This is my favourite for getting rid of them. During the night the snails seem to gather on it, so remove it as early as possible in the morning.
4) Sort of tied in with 3, but during lights out snails seem to gather on the glass and water surface in all my tanks (that have snails), and i find it easy to siphon the blighters out easily.
5)Ofcourse, Clown Loach are an option. If, and only if you have the space to accomadate fully mature adult clown loach!