Li-ion batteries will suffer degraded performance and shortened life if not cared for properly.
If they are overcharged Li-ion cells can explode, hence, the reason why these batteries are fitted with control circuitry.
On the other hand they don't suffer the 'memory' effect of a NiCad or NiMh type battery.
The two biggest factors which will kill a Li-Ion battery are high temps and storing them fully charged.
A typical 6 cell laptop battery will have a life of around 600 charge cycles (some more, some less) if you leave the battery in the computer fully charged whilst using mains power then you are exposing it to the high temps in the laptop, it is kept fully charged and every time it loses a small amount of charge the charging circuitry will top it back up again.
I work with batteries regularly in my job and we did a trial with two new laptops, both identical and running on an 11.1V, 4700mAH, 53WH Capacity, 6 Cell Li-Ion battery. Initially they gave nearly 4 1/2 hours working time. After 8 months the one that was left in the laptop all the time and kept on mains all the time it was in the workshop had dropped to 2 1/2 hours life and then the control circuitry failed.
The one which we took the battery out of whenever it was on mains and was stored with 40% charge is giving 4h 10m life after the same length of time.
The recommendations from the battery manufacturer are to charge the battery once it reaches 20% charge left, if storing it out of the computer for more than 48 hours let it reach 40% charge before removing it and to avoid high temps.
We did want to have a proper look at the charging control circuit in the failed battery as it has been rumoured a number of manufacturers build in a failure after a set number of charge cycles, however, the circuit board was conveniently encased in resin. There definitely appeared to be far more components on the board than would be needed for a simple charging controller. And all the cells in the battery were still able to recieve and hold a charge proving the fault was with the controller.