What are the torque limits of gears?
Do I have to worry about breaking any gears due to excessive torque?


LEGO Gears are one of the strongest LEGO components. When you apply great amounts of torque, they may slip or grind, but never break.


  Do I have to worry about gears slipping (skipping teeth) due to high
  torque?


If you apply high amounts of torque, your gears will slip. This happens even with moderately high amounts. They may also slide down the axle and grind the side of the other gear, or the axle.


  Has anyone performed experimental (destructive) tests to quantify the
  maximum torque these gears can withstand? Order of magnitude is OK -
  will the gears break at 1 N.cm, 10 N.cm, 100 N.cm, ... ?


Your gears will withstand the torque quite well - it's probably other components, like the axles and beams, that will give way first. Don't worry about breaking the gears - the worst situation might be that an axle or two might bend.