Almost all Li(Ion|Poly|FePO) batteries currently don't have “memory effect” when you charge them repeatedly. The only problem happens when you drain the battery below minimum voltage, then it will lose its capacity.
LiIon batteries do suffer from wear from normal usage. The more change/discharge cycles, the lower the capacity. If it is exposed to heat, that damages it. I'm told that leaving it fully charged a lot is also bad for it, because that allegedly puts more stress on the battery than when it is at 90% full.
There is a lot to be desired from current battery technology.
There is a lot to be desired from current battery technology.