In general, is it better to wait until the cell phone battery is all the way run down until you charge it or is it ok to charge it once a day if it's only a little run down?

Depends on the battery it uses. If it is a nicad then yes better to discharge it before recharging. If it is a MH battery then no they will not develop a memmory with short charge/discharge cycles. The only thing is MH batteries do not like to be left on the charger. Charge them up, and remove them. Their life is shorten when you leave them on trickle charge. Robert

How about Li-Ion and Li-Polymer?

It's a lithium cell battery for a Motorola / Nextel cell phone