There is no problem with charging your phone while it is still on. I never turn off my phone and I charge mine every night while I sleep so it is ready for the next day. Batteries don't last forever, but don't cost too much to replace.
Posted from my CrackBerry at wapforums.crackberry.com
I charge mine about once a week. I bought the extended 2600 mah from seidio and use the standard face in belt clip for it. Works like a charm and the extended back cover actually gives people with larger hands a more secure grip on the phone. Well worth the 50 bucks for the battery and cover.