I just bought a new laptop, 95% of the time I use it sitting on the couch while watching TV, I use the power cord 100% of that time. If I remove the battery, will it last longer, if it doesn't keep charging up.

it doesn't matter, will you keep it in laptop or not. the battery controller will do all work for you.

Li-ion batteries do lose more of their capacity when heated, so keeping the thing in the fridge (not frozen!) would surely make it last longer. Then again, is it worth the hassle? You could just replace the batter after 2 years with something that is cheaper and more efficient at the same time.

if you use the power cord whilst the battery is in it will lessen the life of the battery.
Use the battery until it winds down, then plug the cord it.

Laptop battery life is measured in cycles - the more the better. As k.jacko says, don't run it connected to the mains all the time - the more the battery is charged and discharged the better. This will also ensure that it charges to full capacity as often the battery will develop a 'memory' and not charge/discharge through the full range. Exercise the thing!

Yeah, work that battery baby, work dem buns. But don't let if 'feel the burn', otherwise you'll fry your nuts!
Yeah just to reiterate you initial post, if you DO use the mains all the time, remove the battery, it will save its life.

http://en.wikipedia.org/wiki/Lithium_ion_battery#Guidelines_for_prolonging_Li-ion_battery_life