I've had both and prefer my desktop.
I think the main advantage of a laptop is that it's portable. Try to figure out if you will actually use this feature. I didn't use it too much, so it's really not worth it to me. However, if you want to get online with a laptop, I think you have to get something else so you have Wifi access. If you want to move it around the house and still get internet, you need to have a wireless network set up.
Desktops, as a general rule, are less expensive. My old laptop had screen issues for a while and when I finally took it into Best Buy to get it fixed, they gave me a new computer for free (I had the extended warranty -- cheaper to give me the new comp than to fix it.) fI'm not sure what the problem was exactly with it, but after having that issue, I was a little leary of getting another laptop.
Of course, since BB gave me a free computer, or at least covered the cost up to what I had paid for the laptop, which was like 1700, I picked the best, most expensive, most features computer I could get with that. It has wayyyyyyyyy more space than a laptop (I think I asked my brother about adding it once, he said you'd have to take the dang thing apart to do that). It's actually easier, I think, to get accessories for this.
My desktop is now 4-5 years old. When this sucker finally dies, I'm getting another desktop. Even when I had the laptop, I really only brought it on a trip once, and the internet didn't work, so Mom and I could only watch a movie on there. Aside from that, the only traveling it did was between the dorm and my parents' on the weekend.