Utrecht is a student city, and is very safe.
Still, like almost anywhere, don’t flash your wallet at markets and have a natural caution for pickpockets in the city centre. Unfortunately, bike thefts are a common nuisance, so if you travel by bike, make sure you have good locks and try to bolt your bike to a lamp post or bridge railing if possible. There are also free bike parking places with surveillance in the city center and near the train station.
Please note that you are not allowed to stall your bike in certain areas. If you do, the municipality will take the bike away.