The battery contain a chip that automatically stop the charging when full. It cannot overcharge. This is when the plug led turn red to green.
Second of all, don't use the computer without the battery. The Macbooks are programmed to run at half capacity when the battery is not plugged in and running only on the charger. The reason is simple. It's because, even with the charger, the computer need from time to time an extra amount of power that come from the battery. Normally it isn't the case, but if you are running a big computing task and then it need to access the CD and the Harddrive, the Computer will need the extraboost of power fast, and it take it from the battery.
As for the battery. Keep in mind that it is more affected by electron not moving in it for an extended period of time than charge cycle. Staying the computer always connected to the charger is bad because the battery stays unused. Don't panic, you can use it on the charger for some days, just make sure that every two or three days, you use the battery a bit. Just don't fear using your computer on the battery in class or at you local coffee shop. Some peoples always search for a way to plug the computer, it is bad. If you use the laptop regularly on the go, just don't fear using the battery then and use it plugged at home. If you are still mainly at home, then you should from time to time use it on the battery.
Also, do the calibration every month or two, it help the chip in the battery making a better reading of it's status and when to stop the charging, etc... It is clearly instructed in the Mac OS X help (search BATTERY CALIBRATION). Do it exactly as they say (When you are doing a calibration, it is very important you don't drain the battery in two or three session, the whole point of the calibration is doing it one shot.) and you will not have any problem with your battery life. (except of course you received a defect unit...these things can happen, it's just very unlikely.)
