Nice question.
One thing I seem to do often enough is to "skip" over a game if it is a critical position and I don't have enough time (too small a break, waiting in line at a grocery check-out) to do what I would consider a safe amount of analysis. I've noticed that more often than not, rushing through critical positions is where I either miss forcing lines (I think I mostly stopped hanging pieces in correspondence games, but they still happen once in a while! ) or completely miss a single-motif tactic.
On the other extreme, I rarely ever invested more than 15-20 minutes in total (either one sitting, or multiple across 1-2 days) on one position. I probably do this because that's the longest I'd probably see myself thinking in the OTB tourneys I play in my city anyhow. I've personally seen more deep-thinks result in a terrible candidate move rather than a moment of epiphany so I'm a bit wary about over-thinking a position. Though usually most of the time is spent going back and forth trying to decide which candidate move sucks the least.
I try to not use the analysis board as it becomes a crutch and encourages laziness. Working it in your head is better as you have no excuses about being under time pressure.
Another thing that helped is not to play > 5-10 games at a time ... I used to try to play a lot of games but felt that with the smaller amounts of time per game, I put in, I couldn't really do well against really strong players.
I've been playing here for about a month now and I'm curious how much time and effort people put into their moves in the 'correspondence' style online games? I'm currently playing a game where my opponent blundered his queen in a fashion that was quite careless and he couldn't have done so if he was giving the moves more than a cursory examination.
So my question is how much thought, effort and time do you take to find your next move or plan? Do you play forward using the analysis board? Do you search the position in databases? Do you use the opening explorer? Or, do you play these games with the throw away attitude one might a blitz game and make your moves with shallow examination? I know there are some moves that don't require as much thought - such as forced recaptures and such but that isn't what I'm talking about.
I'm curious to see peoples answer to this and how the answer correlates to their rating.