The Bible of the history of mathematics is Morris Kline's Mathematical Thought From Ancient To Modern Times, but this is really for mathematics students. I think it'd be hard to teach a course from it to non-mathematics majors.
To be honest, I think it'd be really hard to teach such a course to non-mathematics majors PERIOD: How would you explain why Weierstrass's non-differentiable function is important to students who don't know calculus? Even worse, why would such students CARE?
If I was really gung ho to teach such a course I'd take Kline, Stillwell, Bell's Men Of Mathematics and 3 or 4 other texts and use them to write a set of lecture notes for my students. That's how I'D do it.
