I would say that Bangkok is no more dangerous that other big bustling cities when it comes to petty crime and pickpocketing. I think in places like the night markets and on public transport you need to keep your eyes open as busy places are where pick pockets have most opportunity. Also just keep you expensive items out of sight so they don't draw attention to you.
I wouldn't let stories of pickpockting put you off going to Bangkok. It is a really awesome city and as long as you are careful and take the necessary precautions you will be just fine. I really had no problems and didn't feel unsafe at all in Bangkok.
For a little more general information check out the Safety in Thailand page.