How i understand it. (i could be wrong) The types of battery's that are used now it doesn't effect the the battery to leave it plugged in all the time.
If you remove the battery it wouldn't have any effect either just the wear from taking it in and out.
If the the power fails and the Laptop is plugged into A/C power without the battery the laptop will shutdown. This can cause data corruption.
My suggestion is just to leave the battery in while leaving it plugged in.