Going the way of Blockbuster, for a US reference. In the same way video stores were/are dropping off because of the ability of people to watch movies in a more convenient/cheaper way (PPV and Cable's On Demand was the big thing at the time), so too are gamers getting games in a cheaper/more convenient way, typically through simply purchasing and downloading them online (even on consoles).
We had Blockbuster in the UK too. I still have PS2 games and DVDs I never returned.
We don't have Gamestop here, but there is definitely something happening with our game shops too. Gamestation, which used to be the most popular, is dying a painful death. GAME is doing ok but only because they're raising prices higher and higher to stay afloat.
The only one that keeps growing is Grainger Games. The first shop opened not too far away from me and now they're all over the country because they sell at ridiculously low prices. Gamestation was always £2-3 cheaper than GAME, but Grainger Games is £10 cheaper than both, more often than not.
Gamestop is going the way of the record store