It depends a bit on the kind of portrait you want to take, but there are two key things you want to do regardless:

1. Not distort your subject. If you're too close to the subject things get warped, so whilst using your wide-angle and getting right up to the nose of your subject may produce an amusing result, it's seldom what you want (but as with all things, it can be great when used sparingly).
2. Throw the background out of focus, drawing attention to your subject.

Bearing in mind that you want to be stood a reasonable distance from the subject to avoid the first issue, for a head-and-shoulders type shot, you'd normally be looking at something that's the full-frame equivalent of 80-85mm, so about 50mm on an APS-C sensor with a crop-factor of 1.6x (Canon).

For a 3/4s length type shot you'll want to be using a wider lens; something like a 50mm on a full-frame body, so about 35mm on a 1.6x crop sensor. You'll get more depth of field with the shorter lens, so may need to ensure the subject is far enough from the background so you can still throw it out of focus. Needless to say fast primes are the norm for portraiture.