Obviously, this is a Live Chess question, I would think ... seeing as you only have Live Chess games in your archive.
Some players have lag, making their first move particularly slow. It's totally up to you how long you'll wait before aborting the game, but give it a few seconds for sure. But, again, it's up to you. I usually give a player 20 to 25 seconds ... if no move by then, I'll likely press the Abort Game button.
I am sorry about my post. What I meant was( I am just starting to play again) if I use one of the standard openings and my opponent responds with a non standard reply, do I continue on with the opening moves?
There are a few system-like openings for which such a response may work. For example, if one is playing the Colle with White, one can often get away with playing the first 6 or 7 moves without a great deal of regard for the moves made by one's opponent (unless a capture opportunity is included).
However, in the main, playing blindly one's pet moves without regard for the non-standard replies of the opponent is usually non-optimal, if not outright foolish. What if you opponent presents you with a fabulous winning opportunity by his/her non-standard move? You would not want to ignore that. Even if the non-standard reply is not immediately losing, one should identify the imbalances created by the move (to use Silman's nomenclature) and respond accordingly.
Alas, the rules of chess are simple; the mastery of the game is beyond the vast majority of us.
Best wishes.
Actually if your opponents first move is bad enough that gives you an extra tempo move to develop major pieces.
What if you play an opening and the opponent doesn't respond with the moves right away?