Lithium-Ion batteries are very lightweight and small for the capacity (mAh) they hold. I don't think they can deliver the same kind of current (amps) that Ni-MH and Ni-Cd can deliver though, so they're not as suitable for high draw devices.
I'm not sure a single cell can be ruined by fully discharging it, but a cell that's in a pack can be destroyed by reversing the polarity. This happens if one cell develops a lower capacity over time and then runs down completely while the other cells are still able to deliver some power. The dead cell is essentially charged backwards by the other cells that still have power, thus reversing the polarity, killing a cell and rendering the battery pack useless.
The best way to prevent this, is to just drop the pack in the charger as soon as the voltage starts to drop, instead of attempting to fully drain the battery. For example, on a cordless drill, recharge when it starts to slow down (it is essentially dead at that point, so you wont be contributing to any memory effect). Do not stand there and run the motor until it stops completely.