I was always told that the NiCad batteries always needed to be
discharged almost completely or they would develop a charging memory
and not charge properly, and this would shorten their life. I know
this was accurate, and covered all nicad cell batteries, cordless
tools, and more.

Now we seem to be seeing a lot of these lithium batteries in
cellphones and other things. should these also be discharged on
occasion, or can they just be charged on a regular basis before they
completely drain?

I'm asking because the lithium battery in my cellphone is getting
weak, and wont hold a charge very long. I have never intentionally
let it totally drain. Most of the time I just plug it in after a days
use. It seems it is now draining from a full charge even with the
phone shut off, (I dont use it often), it will be dead after sitting a
week and not being turned on all during that week.