What do you think about between moves?

The most important thing in chess must surely be how we think, yet I have never seen anything in a book on this. Obviously, when it is our move we think about possible combinations, and also positional issues. But is it prudent to have a checklist - am I pinned, can I be forked, etc? I constantly miss these tactical things because I think too much about what I am wanting to do, and don't think enough about my opponent. And what about when it is his/her move? Is that the time to relax, stand back, and think about strategy, where the overall game is going? Or do you find it is better to put yourself in your opponent's shoes, and ask yourself how the position looks to them?

I'm not suggesting there is one answer to this, but it would be interesting to hear if and how people allocate thinking time.