Considering its size, Bangkok is a relatively safe city. But you should be smart: don't wander down dark alleyways alone and always protect against theft (use a hotel safe and conceal valuables).
You are more likely to be conned out of your money than have it forcibly removed. Be wary of friendly strangers offering touring advice: this is usually a long and costly introduction to the gem scams, in which travellers are sold worthless jewels and jewellery for a king's ransom. Tuk tuk drivers offering