Bihar has a terrible reputation for crime and banditry or dacoity, to use the Indian word, with armed bandits recently taking to robbing moving trains, and there were 55 cases of hijackings for ransom and 2,480 for other reasons! reported in 2008. The situation is steadily improving though, with crime statistics for the most serious offences dropping the last 3 years in a row and, in absolute numbers, crime against foreigners remains comparably low compared to states popular with international tourists. So while reality may not be quite as grim as the horror stories you'll hear from non-Biharis, it's still advisable to keep a low profile and to avoid overnight travel on the roads. A low-level Naxalite Maoist Communistinsurgency continues to bubble in the southern parts of the state, but the tourist is unlikely to venture into the affected regions.
Public transportation systems, like trains and buses, are generally over crowded. Trains in India are generally prone to theft, so it's wise to lock your luggage to the seat in the carriage and keep more aware than usual.