To add to what Kappy said, it will not harm your laptop to leave the AC Adapter plugged in at all times, and it will be a good backup (in case of power failure etc) to have your battery in place as well. This is what I do with both my MacBook and Dell XPS m140.
I will periodically un-attach the AC Adapter and use the laptop with the battery alone, or even just let it stay in sleep mode while I am not using it and let the battery slowly drain away. Then when it gets down to a low percent of power (10-20 % maybe), then I will plug the AC back in and let it charge up again.
I do this once a week or so, just to keep the battery's power moving out and new power in, and I might re-calibrate (spelling?) the battery once every couple months to help keep the battery "knowing what it's full capacity is" and therefore keeping the battery life up to a more full capacity and for a longer lifespan...
That's one of the benefits of using a laptop as a desktop replacement actually. You can move it around with it's small form factor and lighter weight, you can use it anywhere with the battery and having bluetooth and WiFi to use for Internet/accessories/PDA and Cellphone connections, and the battery can act like a built-in backup power supply unit (PSU) which is not just good for storms and other power outtages, but even if you just want to move the location of where you have your laptop (from one room to another) while it is turned on and doing stuff... You can go ahead and unplug that AC Adapter, move it and then plug it back in if you wish to do so, and during that time, your computer kept on doing it's thing (can your desktop do that?) with maybe the only effect being that (depending on your system settings), your screen's display might have dimmed for a couple minutes - if you have it set to dim to a lower brightness amount for battery power compared to AC Adapter power.
Also, I have heard (like many others have) that if you never actually use your battery, that it will die quickly from not
enough use, but if you are constantly recharging your battery, you can expect it to slowly lose what used to be it's full capacity (in the long run, should last 2-3 years anyways I would guess) but one would assume that only recharging your battery once a week or so and using AC power with it for the most part would extend the life of you battery (and if you don't like to use it alot, then it makes sense to not want to have to purchase a replacement battery after 2 years or so, just so you can have one available if/when needed).
I can't say more specifically what the effect is to do this middle ground option, but as long as your battery gets a recharging a few times a month that will be enough to keep it holding power. My GameBoy Advance SP came with a little booklet saying that the internal rechargable battery it has inside (which cannot be replaced by the user) has so many charge cycles in it. Basically, that after so many cycles, the battery capacity will not be as much as it was brand new, and slowly over time the battery will not charge and store as much power inside it, and eventually after the estimated number of cycles (which was only the "guarantee" #) that it, the battery, could totally die and have lived it's full lifespan (compared to it being a bad defective battery). Cell phone batteries often act like this too, so one would assume that laptop batteries could as well.
If a battery had say 400 or so recharge cycles in it (like the GBA SP), and you were using it everyday and needing to recharge it everyday or 2 in the beginning, after half a year you might need to charge it twice as often in the same amount of time, and let's say you use it a bit less often then for the next 6 months, that battery with 400 cycles could last possibly for only *1 Year or so* (if using it so much that you were constantly charging it). If you used it less often, say a couple times per month, and only needed to charge it once per month, then it could last you for up to 5-10 years easily. I'm sure there would be other factors to affect it all, but as a basic comparison, it shows that it could last MUCH longer with just simple basic use every now and then. To be honest, the # I came up with was actually more like 30 years, but I cut it down alot to try and allow for the craziness that a battery for a GBA SP could last 30 years with only a regular "once a month" use...