With a direct flight, you should be fine. I've flown into and out of STT, going to and coming from the states and other Caribbean islands, and never had a problem. Although, none of my flights were on Continental, so I can't speak to their service. When I moved down here, I checked two extremely large suitcases, and had three connections, from what I remember, and the bags arrived just fine. If you are able to pack everything you need in a carry on though, I'd do that, just for peace of mind and to save time you would spend waiting for your luggage to come out.
Also, from what I've heard, if you are staying on St. John, the airline will bring your luggage over here, but you have to meet them at the ferry dock in Cruz Bay to pick it up. Hope this helps.

No problems with checked baggage whatsoever. Are you sure you can take EVERYTHING on board? What with all the liquid restrictions, etc. Have a great time!

I think the chances of lost luggage on a direct flight are slim, especially if you check in early.

Well, I meant if there weren't restrictions, we could fit everything. But even going to the CB dock is OK. Thanks for the replies.

Andrea: Wow, 3 connections?

Yep, I believe it was three from what I can remember...I used to be big on sacrificing personal comfort in order to save money (go figure...more connections = cheaper ticket). I was flying out of Columbus, Ohio, which isn't a major hub, so of course getting to a major hub adds at least one connection.