I think it's ugly, and when I see it in use it seems unprofessional somehow. It's certainly non-standard, and if someone recognizes it, it says "This was done in TeX". I don't like advertising the process when the point is the end-product, so unless I was a big fan of the appearance of Computer Modern I wouldn't use it. If you prefer Helvetica or something, use that, but to just leave it in CM feels lazy - if you care about how your resume looks, shouldn't you care what font it's in?

If CM is your favorite thing in the world, then certainly go ahead and use it of course. I just don't like it.