Aside from the distortion artifacts, one of the biggest problems that results from clipping is a loss of dynamic range. Remember that the dynamic range of a signal is effectively the difference between the maximum output level and the noise floor. When you clip a waveform, you lower the maximum sample value, which lowers the output level and reduces dynamic range.
This can happen especially when you amplify a signal. Amplification increases all parts of a signal, including its noise floor and its maximum value. Normally, these two values increase by the same amount, so the ratio between them stays the same and dynamic range is unaffected. Unfortunately, a signal that is amplified too much has to clip at the top end, and that's when DR suffers.
So the moral here is don't overamplify your music, right? That seems easy enough. The problem is that popular recording studios don't listen. Recall that, superficially, louder music sounds better. Better sounding music sells more discs, and so it pays for the studios to master their music as close to the clipping level as possible. "But wait," the studio says, "most people are tone-deaf anyway. We can get it just a little louder than our competition if we clip a little bit off of the peaks." The competition responds in kind, clipping just a little more, and the result (as Larry scooped me on) is why popular music has terrible dynamic range.
The following articles tell the sad story far better than I can. I encourage you to give them a read.
And one of my favorite illustrations: http://recforums.prosoundweb.com/index.php/mv/msg/4286/0/0/0/
And now you know why serious audio aficionados stick to the classics. :)