No, it´s a bad idea. You loose your UPS (uninteruptable power source), which means you put an unnecessary risk on your data. At least if using the notebook for serious work, there is no good reason to do so.
Concerning the battery life: The Li-Ion Batteries loose capacity due higher temperatures while recharging. Therefore some people say, it is better to remove the battery. However, I don´t know about other notebooks, but on my Vaio FS 115 the battery is constantly the coldest part on the notebook while not recharging, which means, once it is fully recharged, it won´t get any more energy from the power-supply anyway. So there isn´t a really good reason to remove the battery.
