Most parts of Thailand are quite safe, but of course there are dangerous areas, and for the last 8 years there has also been a lot of political unrest and violence. This doesn't usually involve visitors, but of course it adds to the risks. So altogether it is best to be vigilant.
The major danger is from street thieves, pickpockets and sometimes muggers, so the first thing is to make sure your passport and all important documents are safe. Carry them where they won't be easily found, or leave them at your hotel if you are sure there is a perfectly secure place to do so. You should also make copies of everything and keep the copies safe.
Don't wear anything that looks valuable or show your money in public. Be very careful in talking to strangers, as there have been cases of trickery, such as the offer of drugged drinks, in order to rob a visitor. It's much better not to go anywhere with people you don't know. You should also be very careful when paying by credit card - don't let the card be taken out of your sight, and check all receipts etc very carefully.
You can find more safety tips here.