Nope you really should not. Most batteries are lithium ion batteries that develop a memory over time. I learned that the hard way. I always left my laptop plugged in, and in a year my battery was completely dead. From what I know, you should do a complete cycle of the battery at least once a month. That means at least once a month, drain the battery to empty and charge it up again. Dont cycle too often though because that too shortens battery life spans... Soo just keep in moderation. Dont always leave it plugged in, but dont always rely only on your battery either.
is it good to leave a lapstop hooked up to ac power for several days?