As a low rated player myself, I often see people play h6 as black before playing Nf6, presumably to stop pins on g5 and things like the Fried Liver. Example:
[fen ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 h6?!
I keep hearing that such moves are an unnecessary waste of time, which would be better spent developing pieces.
Is h6 to allow the Knight to move to f6 justified? Should I be developing it to f6 at all?
In addition to the useful points in Scounge's answer, I'd add that often the move ...h6 is a waste of time because it's being played at the wrong moment. To use an example from an opening I am familiar with, I play the Scotch Gambit and often find my opponents play this:
[fen ""]
1. e4 e5 2. Nf3 Nc6 3. d4 exd4 4. Bc4 h6
Now, if your main aim is to avoid a knight pin after ...Nf6 or you want to stop Ng5 then this seems logical, but the move is simply bad for several reasons:
Ng5 or Bf5 in this position. Without going into too much irrelevant theory, White isn't playing with a pawn down in order to start an attack but instead to speed up development and hopefully then make something of it. These points should lead you to conclude that allowing a move to f5 is less of a worry at this stage, and you should instead play something that develops naturally (FWIW 4...Nf6 is the book move in the above position). You can apply to the same reasoning to other openings, even though the specific things to consider are almost certainly going to be different (e.g. in the position in the question white isn't playing down a pawn, but instead has different ideas in mind).
Indeed, you'll find if you look at a lot of opening theory that the moves h3 and h6 do appear quite a lot, but they appear at very specific points where that player has nothing more useful they could be doing or there is a specific impending attack that they want to defuse.
The thing with h6 is that, in the opening, the move has one purpose for Black: prevent White from placing a piece on g5.
The drawbacks of the move are that:
It's a tempo investment. Tempos are important not to waste in, for example, open positions, where it is good to get your pieces out to active squares as early as possible.
It potentially weakens your kingside if you decide to castle short. A pawn on h6 can become a target for a piece sacrifice if White decides to launch a kingside attack.
So basically, you shouldn't make the move h6 out of habit. It should be played after carefully considering the consequences of letting an enemy piece reach g5. Does White even want to play a light piece to g5? If not, then why waste the tempo?
This of course applies to the pawn push h3 in the opening for White, and also in some sense the pawn pushes a3 and a6, although the latter two can often have other purposes as well, as in the Sicilian, for example.
The way you've described h6, preventing the annoying Bg5 pin, is called a prophylactic move. They definitely have their uses, and you often see both sides going h3 and h6 after castling later in the game to prevent a later back-rank checkmate, BUT every stage of the game has its own priorities. In the opening, the focus is on establishing a center, developing your pieces, and castling. h6 this early on doesn't help accomplish any of these three objectives and as such should be considered a weak move. Look at it in this light, White generally has a small advantage in the opening by virtue of having the first move. h6 is, in the opening, essentially a do-nothing move, which can only put white further in the drivers seat.
Also as a rule of thumb, Bg5 pins are only worth preventing if you've already developed your dark-square bishop with Bc5 or Bb4 (so that you don't want to play Be7) and you cannot break the pin with a queen move e.g., Qd6.
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.O-O Nf6 5.Re1 O-O 6.d3 h6 {You might want to consider playing h6 here, now black is mostly developed, and has his bishop on c5, so Bg5 could potentially be annoying}
Actually each level of play has its own valid rules which become invalid on a higher level. I recommend sticking with "inferior" moves as long as they bring success against your usual opponents, no matter what the stronger players have to say. After you progress, you will outgrow the rule and will no longer ask.
Play a3/a6 type of prophylactic move only if it's in your opening preparation, or after you have fully developed (ie rooks connected).
If not, find ways to live with Bb5/Nb5 and develop first. As in your case, Nf6 is playable -- it doesn't always lead to Fried Liver. And even if you allow Nxf7, you are not lost and it'll be a good defense exercise
Sometimes it has a bigger idea behind it, maybe preventing a certain dangerous knight from coming to g5 and possibly preparing a retreat square for a bishop. I actually used to play this myself when I was at my first month to chess because I didn't know how to otherwise defend against Ng5 with threat to the f7 pawn (I did not know about the possible temporary pawn sacrifice with d5, exd5, followed by, say, Na5.
But generally it is not a good move if it doesn't prevent a threat that CAN'T be prevented otherwise (Ng5 can easily be neutralized if played).
To a aggressive player(like me), or to any other players, it is just wasting a move, it is better to develop to f6, if you are afraid of the fried liver attack/lolli, try this line, it is a messy line, but black gets more development at the end:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Na5 6. Bb5+ c6 7. dxc6 bxc6 8. Qf3 Be7 9. Bxc6+ Nxc6 10. Qxc6+ Bd7 11. Qf3 O-O
However, if you dislike these kinds of positions, it is your choice to play h6 to prevent it, and it is totally fine, it is still playable as black.
The only time when h6/h3 is normally played is when there a backrank mate threat or you want to start a kingside pawn storm(a3/a6 for queenside), sometimes when you play sicilian, you world play a6 because of the amount of pressure on b5 and a white bishop there would just make black's life harder, I can't currently think of reasons to play a3/h3/a6/h6(related moves) other than these, if I come across any, I'll edit this.
