user4016: I looked around and could not find an answer for this.
I've studied a pretty good amount of opening theory and so I know the "correct" moves for some basic lines.  Most e4 openings and a fair amount of Nimzo-Indian, Pirc, and QGD for D4.
The thing of it is, I often play opponents who have not studied these lines.  So they play the "wrong" moves and I'm not sure how to proceed.
Is it best for me to stop and eat clock time figuring out why the wrong move is wrong?  Or should I keep playing my same opening even though I might be putting myself deeper into a hole?

user21234: Nothing. You stick to chess principles, and while you are learning openings you need to study why openings are played in a way they are, whats the idea behind the opening.

user20721: Because it is a game and a contest/struggle.  The opponent makes moves that are good for him not the moves in the favorite line you memorized.
Stop figuring out why his move is 'wrong' and figure out what your best move and plan is and then do that.  Chances are that his move is quite good even if not the theoretical best.  
You do not keep making your same memorized moves.  You do not waste time figuring out why his move is wrong.  You spend some time to figure out what is a good move for you. 
Using principles and checking tactics is more useful than obsessing about book lines you think are 'correct'.
You have beginners syndrome.  When you improve and gain experience these sorts of moves will not bother you. 

user17740: Just a side note. Because your opponent makes a non book move does not mean it can be punished. This was a big realization for me because I always wanted to punish non book moves.
Especially, if you are playing Black. White has a wide range of moves to choose from. Some may give him a .25 advantage while another is only .10. It is clear that you cannot punish the .10 advantage. He still has a small advantage from having the first move.
My experience is that most non book moves are not totally wrong. So treat them with respect and simply try to find your best plan and best move. Stop trying to punish these moves because that is largely a waste of time. If they totally blunder that is another matter and easily dealt with.

user11609: Nothing is ever certain, but when you are in position that was played in thousand of high class games, any deviation is virtually always dubious move. On the other hand in position which was played in lets say just 10 high class games, novelty is still more probably to be dubious, but it is nowhere close to be certain. Also there can be more equally strong moves in later stages of a game then in very beginning when you run to fight for centre. Taking time with first new position is good thing to do. Compare move with your knowledge of other moves and try to build good plan. No reason to play autopilot in position you don't know. No two positions are really similar, today chess is pretty concrete.

user15221: 
Is it best for me to stop and eat clock time figuring out why the wrong move is wrong?

No, you should learn before the match what the responses to deviations are. If you don't know why deviations are "wrong" and how to punish them, then you don't really know the opening.  

user9025: It sounds like you're a beginner. As such, you should be focusing more on tactics than openings.
First, just because they play a move that's not in your book, doesn't mean it's "wrong". It may be an older line that's not in modern opening books, or just not in the books you have.
That being said, to answer your question, it depends on the opening. In a slow, closed or positional openings, it's not likely to matter too much, when your opponent deviates from your book, just adjust your plans as necessary. If it's a gambit, or tactical opening, you should take some time to check to see if it's a blunder.

4016: <p>I looked around and could not find an answer for this.</p>

<p>I've studied a pretty good amount of opening theory and so I know the "correct" moves for some basic lines.  Most e4 openings and a fair amount of Nimzo-Indian, Pirc, and QGD for D4.</p>

<p>The thing of it is, I often play opponents who have not studied these lines.  So they play the "wrong" moves and I'm not sure how to proceed.</p>

<p>Is it best for me to stop and eat clock time figuring out why the wrong move is wrong?  Or should I keep playing my same opening even though I might be putting myself deeper into a hole?</p>
 21234: <p>Nothing. You stick to chess principles, and while you are learning openings you need to study why openings are played in a way they are, whats the idea behind the opening.</p>
 20721: <p>Because it is a game and a contest/struggle.  The opponent makes moves that are good for him not the moves in the favorite line you memorized.</p>

<p>Stop figuring out why his move is 'wrong' and figure out what your best move and plan is and then do that.  Chances are that his move is quite good even if not the theoretical best.  </p>

<p>You do not keep making your same memorized moves.  You do not waste time figuring out why his move is wrong.  You spend some time to figure out what is a good move for you. </p>

<p>Using principles and checking tactics is more useful than obsessing about book lines you think are 'correct'.</p>

<p>You have beginners syndrome.  When you improve and gain experience these sorts of moves will not bother you. </p>
 17740: <p>Just a side note. Because your opponent makes a non book move does not mean it can be punished. This was a big realization for me because I always wanted to punish non book moves.</p>
<p>Especially, if you are playing Black. White has a wide range of moves to choose from. Some may give him a .25 advantage while another is only .10. It is clear that you cannot punish the .10 advantage. He still has a small advantage from having the first move.</p>
<p>My experience is that most non book moves are not totally wrong. So treat them with respect and simply try to find your best plan and best move. Stop trying to punish these moves because that is largely a waste of time. If they totally blunder that is another matter and easily dealt with.</p>
 11609: <p>Nothing is ever certain, but when you are in position that was played in thousand of high class games, any deviation is virtually always dubious move. On the other hand in position which was played in lets say just 10 high class games, novelty is still more probably to be dubious, but it is nowhere close to be certain. Also there can be more equally strong moves in later stages of a game then in very beginning when you run to fight for centre. Taking time with first new position is good thing to do. Compare move with your knowledge of other moves and try to build good plan. No reason to play autopilot in position you don't know. No two positions are really similar, today chess is pretty concrete.</p>
 15221: <blockquote>
  <p>Is it best for me to stop and eat clock time figuring out why the wrong move is wrong?</p>
</blockquote>

<p>No, you should learn before the match what the responses to deviations are. If you don't know why deviations are "wrong" and how to punish them, then you don't really know the opening.  </p>
 9025: <p>It sounds like you're a beginner. As such, you should be focusing more on tactics than openings.</p>

<p>First, just because they play a move that's not in your book, doesn't mean it's "wrong". It may be an older line that's not in modern opening books, or just not in the books you have.</p>

<p>That being said, to answer your question, it depends on the opening. In a slow, closed or positional openings, it's not likely to matter too much, when your opponent deviates from your book, just adjust your plans as necessary. If it's a gambit, or tactical opening, you should take some time to check to see if it's a blunder.</p>
