OK, here goes:
1. Mash - I start measuring at the 45 minute mark to check for progress. As conversion progresses the gravity of the mash increases. This reading gives me an early indication as to whether I'm going to be high or low. I know the expected ratio of gravity between first and second runnings. So, I can immediately tell when conversion has reached the desired point.
2. First runnings - I batch sparge in two batches of equal size (generally 4.04 gallons each). I take temp, gravity, and volume measurements of each set of runnings.
3. Second runnings - as I said above, I know what this should be based on expected preboil Gravity.
4. Pre-boil - so I can make any adjustments for gravity, boil-off, or hops.
5. I take 4-6 readings during the boil. This allows me to monitor boil-off and accurately predict the total boil-time. This allows me to ensure that my hop additions enter the wort with the correct remaining time. This way I end up with the final wort gravity expected, and the hops have been in exactly the right duration.
6. Post-boil before I start the chiller.
7. Post-chill before transferring to fermenter.
8. After pitching yeast starter. The starter will dillute the gravity a tad.
9. Every day during the ferment.
10. After transfer to the keg.
NOTE: I take volume, temperature, and gravity measurements at every point I can. I calculate total points at every step on the hot side. I write down the raw measurements and THEN I correct for any temperature curve (volume, hydrometer). That way, if I screw up the math, I have the original data to rework from. I cross-check all measurements against previous measurements and re-do if something doesn't make sense.