Ok this the false information is really aggravating me now. Rolling Rock however is correct whereas Makaroni is completely wrong.
Li-on and Li-polymer batteries should never be completely discharged or it would effectively murder the capacity, and should never be overcharged or they would explode. So chargers are designed to not overcharge the battery by stopping the charging process when the battery is at capacity. Now, the information that battery life is reduced by keeping it plugged in and the concept of what a Cycle is is whats driving me nuts. A cycle is when a battery is discharged by some amount, and then recharged, it doesn't have to be a full discharge. The percentage that it has been discharged effets how many cycles a battery can be recharged for over its life time. A battery that has been recharged after a 20% discharge over and over again vs a battery that has been discharged 50% and recharged, over and over again...the 20% discharged battery will last longer. (I can find references for this information if you really want it)
If you keep a battery plugged in to preserve its life, technically its life should be longer than if you discharged it by some amount. (This is not factoring in heat generated) I don't really have a comment on leaving it plugged in 24/7...but wikipedia says "The software of a typical smart phone, for example, learns how to accurately gauge the battery's life by watching it discharge and leaving it on the charger produces a series of "micro discharges" that the software can watch and learn from."
Also the degradation of lithium ion batteries is also highly dependent on heat. I don't have a comment on the heat generated from charging a battery but I just wanted to get all the misinformation about li-on batterys out of here
High charge levels and elevated temperatures (whether from charging or ambient air) hasten capacity loss <---Straight from wikipedia.
The need to "condition" NiCd and NiMH batteries has incorrectly leaked into folklore surrounding Li-on batteries. The recommendation for the older technologies is to leave the device plugged in for seven or eight hours, even if fully charged.[118] This may be a confusion of battery software calibration instructions with the "conditioning" instructions for NiCd and NiMH batteries.[119] The software of a typical smart phone, for example, learns how to accurately gauge the battery's life by watching it discharge and leaving it on the charger produces a series of "micro discharges" that the software can watch and learn from. <--- also wikipedia
The last paragraph specifically addresses smart phones.