Keeping Li-ion batteries at high temperatures and at a high state of charge (high capacity, high voltage) promotes non-recoverable capacity loss
[1].
Personally, despite the consequences, I keep the battery in my laptop with the AC power adapter connected, whether it's charging or fully charged. I used to remove the battery, but there has been many occasions where the power adapter has been accidentally unplugged from the laptop, resulting in the loss of the session and all unsaved work (frustrating to say the least). In addition, keeping the battery in the laptop has saved my bacon in power brownouts and dropouts (kind of like a basic Uninteruptable Power Supply).
I recall someone saying to buy an extra battery and store it. It is not a good idea to stockpile Li-ion batteries because they start deteriorating the moment they have been produced and leave the factory.
The following is a good referenced article about laptop batteries, with information about the danger of Li-ion batteries, how to increase runtime, prolonging battery life and how to go about buying a new laptop battery:
h! - Power That Laptop!