There has been, as far as I know, one single case of tourists being attacked (and killed) by militant Islamists, which happened a few years ago. So statistically it's probably safer than a lot of places. There is significant resistance to the regime under the surface, but everything is still held together by an aging, kleptocratic authoritarian. So in some sense it's a volatile place, and the situation could obviously change significantly in a matter of hours or days in a way that's unlikely to happen in, say, Europe. (Or at least Europe of five years ago...)

I think it is still a very safe place to visit, and many tourists, including Americans, visit every year. Extreme things can happen anywhere. The likelihood of getting mugged I'd say is effectively zero, at least compared to London or Barcelona.