I have a custom built gaming computer as does my parnter (though her's is currently undergoing maintainance).
They both have fairly good graphics cards, mine is pretty new and cost around £80. Can run most games on full with few framerate issues.
I have a laptop with a ATI4570 built in. runs most games on medium-high with very few issues (not to mention the 3D screen). My partner has a netbook (aspire one) that can barely run minecraft and has a broken trackpad.
We both use the Laptops more.
I much prefer my PC for programming and gaming. It's faster, has 3 Screens and a nicer keyboard. My laptop has a pretty sweet keyboard too (I refused to get a laptop without a proper sized numberpad)
While the desktops are great, and I love them to pieces, They're not as "social" as laptops. I'm lucky in that I had a job a while ago with no bills to pay, so I could afford both, most of my friends, however have laptops for portability (some travel 40 miles to University). When they're round it's just not practical to cram 4 people in a tiny room with 3 computers, much easier to have 4 of us downstairs on sofas and chairs and boxes and whatever else we can muster. Considering we all play minecraft the most together it allows for easy communication, to have something on the TV in the background and it'll run fast on most laptops. I also like playing Games/Document editing on my phone..
I suppose the end result is whatever works for each person. If you need portability either get a desktop pc and a tablet (as my friend is probably doing), or get a laptop. If you're not bothered you can splash out on a desktop and keep a smartphone just incase.