The post that was quoted here has been removedAnother good time is when you don't waste a tempo on the move.
In another thread you asked about the Bg4 pin, you can combine the solutions in the other thread with an h3 here, the bishop on g4 is forced to move, so you don't loose a tempo....
Actually, if your opponent wanted to play Bxf3 then you have lost a tempo, so I guess that h3 works best when you think that Bxf3 is an inferior move.