They still exist, but they're incredibly niche nowadays. Arcades are split up into two categories: small stores that cater to niches, like classic American games or imported modern Japanese games [1][2], or huge chains that specialize in 'family entertainment' [3] that include bowling and food.
The arcade isn't dead yet - there's still plenty of enthusiasm for rhythm and fighting games, which I believe is actually growing. At least among my friend group, it's much more rewarding to face off in person than to be trashtalked by some anonymous gamer on an online console gaming service. Also, when the arcade closes, there's nothing better than just sitting around and chatting for a few hours. Arcades make a fantastic "third place" [4].
[1] http://freeplayrichardson.com/
[2] http://arcadeufo.com/ (disclaimer - owner of this place)