I've never bought a desktop.
I've bought a couple of second hand old Macs to play around with, bought a desktop motherboard and done a "breadboard" sorta thing, and used many desktops. But whenever I've owned a computer I've gone for a laptop just because I like to move around the house and sit on couches when using computers.
If you want to game on it, a laptop is a tougher choice. It'll cost more, it'll need to be internally dusted a lot to keep the fans efficient, and you might need a cooling pad to make playing on it more comfortable. Otherwise you'll find the computer may shut down when it gets too hot.
Getting a desktop is cheaper, and more comfortable for gaming. Its also easier to upgrade a desktop if you wanted to. Of course, you'll need a desk and an office chair, and you'll be stuck in one place. I like moving my computers around, and I pay the price for it. I still get to play GTA IV and Blockland smoothly though. :3