GC is growing, but as Majeski notes, they've got a huge amount of debt. Their story is mixed. On the plus side - they've created an environment where it's less intimidating for newbies to come in and try a guitar. When I began to play again a few years ago (after a multi-decade break) I found many stores intimidating. Guitars were behind the counter and you had to ask for help. At GC, you can walk in, try a dozen guitars and no one will make you feel uncomfortable, regardless of your skill level.
The other thing that helps them is that guitars are very personal purchases. I'll buy an amp or pedal online but when buying a guitar I need to feel it in my hands. If you pick up five copies of the same model Fender Tele, even if they came off the assembly line the same day, each will feel different - the weight, the quality of the fretwork, etc. So, while I make 95% of my purchases online, I buy guitars in person. I've probably bought 6 guitars and 3-4 amps from GC in the past three years (for both my daughter and I).
On the downside, a lot of GCs growth has come at the expense of mom & pop music stores. That's no surprise, of course, but the mom & pop stores provided a level of service that GC typically doesn't offer. So their growth may not be good for the music industry as a whole. But they have the buying power to undercut others in price and they have an online component (both under guitarcenter.com and their sister brand, musiciansfriend.com) to complement their stores.