It depends on how old the laptop is. If it's an old laptop (I'd say 5+ years old), I would remove the battery when it's fully charged. If it's a newer laptop, then you should be fine.
Lithium batteries lose life the more often you charge them to 100% or discharge them to 0%. Those extreme charges and discharges damage the chemistry, reducing the amount of charge the battery can hold. After enough such cycles, the battery only holds enough charge to power the laptop for 5-15 minutes.
http://batteryuniversity.com/learn/article/how_to_prolong_lithium_based_batteries
The problem with older laptops was that because batteries weren't as good back then and laptops consumed more power, manufacturers used the full capacity of the battery. That is, they charged to 100% and discharged to 0%. When you left the battery on the charger, it would charge to 100% and stop charging. Eventually the battery would self-discharge to 99% (usually 20 min-1 hr), and the laptop would automatically charge it back up to 100%. Every time it did this, it would damage the battery. The usual solution was to remove the battery from the laptop when it was at about 80%-90% charge, and put it back only when you needed to use the laptop without AC.
Modern laptops are thrifty enough in their power consumption that most manufacturers now build in usage buffers in the battery. That is, the battery might report it's at 100% to Windows, when it's actually at 90%. If the laptop tops off the battery when it drops to 99%, it's actually only charging from 89% to 90%, and thus doesn't damage the battery (or damages it a lot less than a 99% to 100% charge). Other laptops report to Windows that they already have 5% or 10% wear when new, thus making Windows only charge it to 90% or 95%. You're safe leaving any of these laptops on the charger, little to no risk of damaging the battery.