Bangkok is generally safe for visitors, with a few practical things worth knowing.
Violent crime against tourists is rare; the more common issues are overcharging, scams around gem shops and tuk-tuk tours, and standard big-city pickpocketing in crowded markets.
Road traffic is the most realistic everyday risk — cross at marked crossings where possible and be cautious around motorbike taxis weaving through stopped traffic.
Be wary of anyone outside major sights claiming a temple is closed and offering to take you elsewhere by tuk-tuk — it's a well-known setup that usually ends at a gem or tailor shop.