Hi,
I've been using this circuit to charge my kodak camera's li-ion battery since a few months, and it's result is nice.
My design has 3 leds, one to indicate charging(blink), one to show full battery, and one to indicate battery presence.
Actually it's a composite circuit idea which I made by mixing up a few li-ion battery charger circuits.
The key is a LM358 op-amp IC, S8550 PNP transistor, and a bunch of resistors.
LTC4054 and other dedicated li-ion charger ICs are there, but if it's going to be a DIY project's part, then who wants to miss the less IC and more resistor, capacitor's fun? Surely I don't. You can give 5V supply from wall adapter, or from USB port.
Link to my blog entry: http://www.circuitsdiy.com/simple-lm358 ... n-charger/ (http://www.circuitsdiy.com/simple-lm358-op-amp-based-usb-li-ion-charger/)
Try this, I'm sure you won't be disappointed.
Update: http://circuitsdiy.com/projects/usb-li-ion-charger (http://circuitsdiy.com/projects/usb-li-ion-charger)
Video demo(ignore V/A sync problem): https://www.youtube.com/watch?v=wJ_uI1uWbes (https://www.youtube.com/watch?v=wJ_uI1uWbes)