The advantages to h6 are obvious. Keeping White pieces out of g5, and giving your King an escape square to eliminate back-rank checkmates.
The disadvantages are not quite as obvious. The first problem is that it severely weakens f5, similar to how a6 weakens c5 in openings like the Slav Defense. The reason is simple. The advance of h6 makes it hard to advance the f- or g-pawns safely. If you advance g6, h6 becomes very weak. If you wait for a Knight to come to f5, and only then play g6, h6 hangs unless there is no way for the Knight to get back out. If you advance the f-pawn, the g6-square is very weak. If you advance both the f- and g-pawns, the King becomes airy. The game here shows a prime example of this. I played the White side of a Queen's Gambit Declined, Rubinstein's Variation (where white plays Qc2 instead of Rc1), and Black played an early h6. My Knight is headed for f5, which he stops with g6, but then I win the h-pawn, and roll my Kingside majority down, creating a passed h-pawn to win the endgame.
http://www.charlottechess.com/games2/1116.htm
The second issue with advancing the h-pawn is it creates what is called a hook. White can advance the Kingside pawns, going for g5 to try to break open the Kingside. He needs to do it at a time when h5 is bad, either because it allows g6 and re-creates back rank issues for your King (assuming you have a pawn on g7), or else the h-pawn would just hang if you played it to h5, like if your Q is on e2, and Qxh5 is possible then. Also, pushing your own pawn to h5 before playing g5 (this isn't always possible) would make it impossible for Black to avoid the pawn trade and opening of the King.
The following game was horribly played by both players. White in the Opening, Black in the Middlegame. I had Black, and lost, in this Queen's Indian-esque position (not exactly a Queen's Indian, but similar), and I played h6, and probably shouldn't have. I also shouldn't have retreated the Knight back to d7. Lastly, later on, I had opportunities to attack in the center instead of dumb moves like Rg8 and a5.
The fact that I was beginning to come down with flu-like symptoms with the full effects the following morning probably didn't help either.
http://www.charlottechess.com/games2/1114.htm
So these are 2 prime examples of h6 turning out really bad for Black in Queen's Pawn Openings (a lot of ideas in the QGD also apply to the NID and QID). Of course, there are times when h6 is fine, but you have to understand both scenarios like a fine tooth comb. Many amateurs just think of h6 or a6 (or h3 or a3) as a simple prevention measure, but there's far more to it than just that.
The Tartakower and Lasker Defense have a ...h6 move while the Orthodox Defense doesn't.
It looks like the Orthodox Defense is more solid/safe due to not having a ...h6 move?