I've had my iPhone 3G for about two months now, but in the last week the phone has begun to have issues with charging properly. The phone will not properly show the charge progress on the screen (IE it won't show the meter filling while it's plugged in), but if I restart the phone it will show some progress. The phone will also sometimes say the battery is charged (showing the plug in the small icon in the upper right), but the meter won't be full.
The phone basically seems to stall when charging, sometimes the charge meter jumps in random spurts and other times it just sticks at one point with no change, sometimes a restart will get it to show some progress and other times it won't do anything.
Most of the time I let the phone charge from the USB port/iTunes. Sometimes after a few months the battery seems to not last very long. I fix it by putting it on the wall outlet charger overnight, that seems to solve the problem.