I'd be surprised if there is not a requirement for an egress window from a basement sleeping room in every state. Not only the window, but the window well must be larger. In planning for the possibility of a bedroom in our basement, we had a larger window and window well put in. Of course, once the foundation is poured, cutting out a larger opening is a major undertaking.
Having said that, we had a sleeping room in the basement of our last home for nearly ten years. Enforcement is a bigger issue than safety, IMHO. The code has to address the worst case scenario; an older home, a negligent landlord, a less than savvy tenant. No code official is likely to inspect the house to see if the room is used as a sleeping room. If you know they're coming....
With a good furnace, newer appliances, new wiring, a fire is unlikely. Just don't allow anything capable of starting a fire (matches, etc.) to be taken to the basement. When you sell the house, you cannot claim a bedroom down there unless it meets code.
To clarify a bit, the code requires two exits from a level with a sleeping room. In the case of a basement or second story, that's usually a window. (...and a "ladder" to get up to the window from the basement, or down from the second floor, in which case the fire department provides it). If a basement has two independent exits (rare, but it happens with houses built on a steep slope) then the bedroom window doesn't have to be big enough to crawl through.