I keep my G73SW-A1 plugged in with the battery... been doing this since last August, without any issues. I have noticed that once in a while the battery charge drops to around 95% automatically, then charges up again. I do use the notebook on battery only for like a couple times every week.
I don't see any reason to ever remove the battery (except when servicing the hardware, of course).
At my old job a few people left their laptops plugged in for 6-8 months. When they finally went to take it somewhere the battery was dead. Since then I always recommend at least one discharge cycle a week. If you always game on it, just unplug it before bed one night and leave it on...
Rocking a G53SX-A1 upgraded to 16GB.