Is it best for my laptop battery to keep the computer plugged in whenever possible?

Question

Should I leave it unplugged and let the battery run out sometimes?

Answer 1

Answer DEPENDS on type of battery your laptop uses.
Nickel-Cadnium batteries self-discharge and Metal Hydride batteries do not. So if your laptop battery is the Ni-Cad type and you leave your laptop unused for extended periods of time then sure, use it up and then recharge it. This will prolong it's life. However, if it's a metal hydride battery, which supposedly has no "memory" of previous extent of charge, then you do not have to worry, except during the first charge when you purchased it.
When charging any battery for the very first time, you HAVE TO charge it FULLY.

If you have the Ni-Cad battery and it's fully charged and you use your laptop daily via the electrical outlet as the power source then the battery will NOT be affected in any way because no power will be drawn from the battery and it will not have time to discharge.
In fact, you can use the laptop while plugged into the electrical outlet and still re-charge the battery.
So, if the battery is already fully charged, it will stay fully charged as long as you use the outlet. Therefore, no worries that you are partially discharging the battery and recharging again.
HOWEVER, if you have used the battery only then sure, use it up.

Answer 2

Totally Up To You.