I was just wondering when was the good time to do h3. I don't know if this is a weakness to not make in your pawn structure once you've castled, or a necessary escape root. I usually find myself being careful of backrank checkmates and only playing h3 close to the end, or if I have a lasting advantage.

Any advice is welcome!

Depends on the opening, sometimes h3 is a usefulmove.

Oh, the opening: Usually Ruy Lopez

1.h3!

Sure to catch your opponent off-guard.

The Ruy Lopez doesn't normally call for a early h3. 

Ok, but then should I do it in the midle game, or rather the end game?

As everyone said, it depends on the situation. As a general rule, just make h3 if you really want to push your rival to make a decision, i.e., either be prepared for an exchange on f3 (with at least equality), or push your rival to move his bishop away from the c8-h3 diagonal, which in that concrete position may be vital for you.

Otherwise if there's no other deep purpose on your move, I think playing h3 by playing it is just a wasted move, and a possible weakness for the endgame.

Take care.

The main line does.

 The main line of the Ruy goes like this: 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba5 Nf6 5. 0-0 Be7 6. Re1 b5 7. Bb3 d6 8. c3 0-0 9. h3

To not play this (maybe by 9. d4 instead), invites Bg4 and more pressure & distractions than White had in mind when he started the Ruy. Most White players play 9. h3, where the big breakdown into various systems begins: 9...Na5 (Tchigorin), 9...Nb8 (Breyer), 9...h6 (Smyslov), 9...Bb7 (Zaitzev) etc...

Did you read the thread? He/she correctly responded to the claim that the Ruy Lopez doesn't usually call for h3.

The 9. h3 vs. 9. d4 in the Ruy suggests a decent rule of thumb for whether h2-h3 makes sense in a given position.

You take away ... Bg4 (and to a lesser extent ... Ng4) with h2-h3 when that is clearly going to be the best square for the opposing bishop and allowing it to move there is actually going to pose you with concrete problems.   If you can allow ... Bg4 without having problems, h2-h3 is probably just a wasted move.   There's no sense wasting a move to prevent something that is harmless.

There are middlegame situations where h2-h3 is okay to stave off a back rank threat, or (when ahead) to prevent having to calculate back rank threats.  There's almost always a better, more active move available than to just play h2-h3 against some future threat that hasn't yet materialized.

Thanks for all these comments

I'm going to be keeping this in mind whenever i think of doing h3 or something else. So if I've understood, h3 isn't recommended, except in some situations, in which case I must see if it's really the best I can do.