I do. I opened an iTunes account when I got my iPod four years ago and I think I've bought a total of about 20 songs in that time. I never download music from share sites.
For one thing, I like having the entire album from the artists I like because many times the best material is NOT what the record company chooses to release as the "hits". The record company chooses to release the songs they think will reach the widest audience and make them the most money in the shortest time possible. I'm more interested in the best material.
Second, downloading pirated copies of an artists material doesn't sit well with me. To me, an artist should be compensated for the work they put into writing, recording, and making an album. Yes, I realize some people will attempt to counter that with the classic "sticking it to the rich fat cat record company for screwing the little guy artist and extorting the little guy music buyer" argument. Please, spare me that tired, flawed idiocy. If the artist chooses to give away their music in some way, shape or form, such as free downloads on their website that's one thing. But downloading bootleg copies of their work that is NOT freely made available is theft, plain and simple. Any arguments to the contrary are simply weak justifications to cover up the fact that you're doing it only because you know you won't get caught. You don't walk into Guitar Center and steal a bass because the "fat cats" at Fender make too much money and are screwing poor starving artists by charging too much for their instruments, do you? Of course not. You'd get caught and could do time! When you have the guts to steal your gear from the stores while flipping off the store manager as you walk out of the building, then I'll listen to your arguments about pirating music.

And no, I don't copy CDs from friends. I might borrow one to see if I like it enough to buy it. If I do, I will. If not, I won't. There have been some rare occasions when I didn't want an entire CD and instead only wanted only individual songs, but as I said above those cases are rare.
Third, I like having the entire package - original CD and any and all artwork. Enjoying a little JPG of the album cover that pops up on my MP3 player just isn't the same thing to me.
Fourth, you're guaranteed to get the best audio quality. Downloaded copies may be high quality, but certainly might not be.
That's it off the top of my head. I'm sure I'll also agree with many other reasons others come up with as well.