Nice info kept simple for people new to li-ion cells etc. Cheers HKJ.
I wanted to mention too, that the reason for not over-discharging li-ion cells on a regular basis is not only because it reduces the usable life of the cell, although that is certainly a negative effect of over-discharging. Another big reason is the safety concerns. Sometimes it happens over time, sometimes it can happen immediately, but when this chemistry cell is over-discharged - without going into chemical details - it causes the copper metal (which is used as the current collector at the negative electrode) to dissolve into the electrolyte material inside the battery, and then when it is recharged again the copper can redistribute itself again inside the battery in such a way that it causes a short inside the cell, which can then cause thermal runaway, start a fire etc when the cell or battery is recharged. Again, this doesn't happen when over-discharging, but it creates a situation where the battery is no longer safe when subsequently RE-charged. You might be lucky a hundred times and nothing bad happens, or it might happen the hundredth time recharging, the 50th time, or even the first time recharging after an over-discharge.
So what I'm saying, in a nutshell is: There is also the safety factor involved in over-discharging li-ion cells or batteries. It can be dangerous and should be avoided, not just for the longevity of the cells, but also for safety. Stay safe out there!
-source: Lithium-Ion Batteries Hazard and Use Assessment paper, Fire Protection Research Foundation.