Charging tips on how to keep my cell phone battery long-lasting?

I’m about to get a new mobile phone, and even though this is my 4th one I’m still not sure if when and how often I charge the battery makes a difference as to how long the battery will stay healthy.

I thought Cecil dispelled the “battery memory” myth (at least for modern rechargable batetries), but I can’t find the article in the archives for some reason. Assuming I’m remembering correctly, is this still true, and "topping off’ my phone’s charge every morning via the car charger on my commute to work (about an hour) won’t result in a memory issue or any other problems?

A person selling phones in a Circuit City once told me that letting the battery fully discharge is actually bad for it. Is this true?

How about using the car “quick” charger vs the wall charger? Will that harm the battery in the long term?

Any other tips or info appreciated.

Most modern cell phones use lithium-ion batteries. From this web page:

Thanks! Sounds like topping it off every morning is OK.