Yep, basically no problem mixing tire types, widths, and even diameters. The rear tire will carry more weight and generally wear faster, so that may be a consideration in picking different tires.
The front and rear are exposed to vastly different forces and there may be good reasons for having different tires as a result. On the front a narrow tire with light tread will permit turning with less effort, but on the back this isn't as much of a concern. OTOH, the front tire provides about 3/4ths of your braking ability, so that's an argument for giving it a more substantial (or at least not worn out) tread. In terms of sideways skids on slick/loose surfaces, a front tire skid is likely to result in a more out-of-control situation (ie, more road rash) than a rear tire skid, but it's harder to get the front skidding in the first place, so hard to say how tire style would affect this.
And (probably due mostly to the weight difference), punctures occur in rear tires 2-4 times more often than in front tires.
Of course, on a used bike the tires are apt to be different simply because they were not replaced in pairs. I'd generally say this is of no concern so long as they are roughly equivalent. If the front tire is much "heavier" than the back, though, my inclination would be to swap them.