I agree with Tumpliner - I had a look, and it seems there is really little distinction, except that Americans would prefer "among" and British would prefer "amongst". I suppose it's really a matter of how it sounds to you, eg. "amongst" does sound a bit upper-class.

You know, this is probably not a good answer, but as a native English speaker I will tell you that there probably is a difference, but I don't know what it is. Probably most Americans do not either. Among is much more common. If you say "amongst" you will sound very educated to most people, so you will have to plan on living up to this image.

The difference is that one has "st" on the end and the other doesn't. I am British so I tend to use "amongst" (I think to British people "amongst" sounds much more pleasant than "among"). Both are acceptable though and it does depend on the situation and the register required.

one is more literary (frequently seen in poetry) than the other--e.g. while, whilst; amid, amidst

The amongst is confirmation in writing of the among,which are the same as while and whilst