[sounds]

Good answer. In case anyone wants more detail, wikipedia is a little vague, but has the basic idea right:

"Overdischarge supersaturates lithium cobalt oxide, leading to the production of lithium oxide...deep discharge may short-circuit the cell, in which case recharging would be unsafe."

and

"Overcharge up to 5.2 Volts leads to the synthesis of cobalt(IV) oxide...if overheated or overcharged, Li-ion batteries may suffer thermal runaway and cell rupture. In extreme cases this can lead to combustion."

http://en.wikipedia.org/wiki/Lithium-ion_battery

The possibilitiy of thermal runaway or fire from overcharging is actually fairly likely with Li+ ions, since they will react with any non-inert substance.

The short circuit caused by undercharging can affect other cells in the pack, leading to overheating and combustion.