Actually, Nf6 is the most popular reply to Nf3 -- see the Game Explorer, there are over 123,000 master games that have started that way. (It's also my favored reply.) Black matches White's flexibility, and the game can lead in many different directions.
You don't usually hear of it as a distinct opening system, though, because it's extremely transpositional -- after a few more moves, the game will usually take on the character of some variety of queen-pawn or English opening. A game that starts 1.Nf3 Nf6 2.c4 e6 3.d4 d5 is a Queen's Gambit Declined just the same as a game that followed a more conventional move order.
I have been copying 1. nf3 and play 1...nf6. I figured if he played 2. c4 d5 is some kind of Gruenfield, against 2. g3 it is 2...c5, but I like playing against 2. d4 the most. Now 2...c5!? leads to very interesting positions. It could be a benoni, and white could cerntainly transpose into that if he wanted, but now if 3. dxc5 na6! preparing to recapture. 4. qd4 qa5+ with very interesting positions. If 3. d5 b5 and we have pressure on that pawn. I played this against my friend who is rated over 1800 (This is otb, not online.) in a blitz game. He paused, then pushed. Clearly not many people study it.