It depends. You can run most games on a lot of laptops, just depends on how well you want it to run. I can run the Stars Wars MMO on my laptop doesn't have any piece of gaming hardware whatsoever and all of the parts are almost 5 years old. I just have to run everything on lower settings, still looks fine though.
If you want to do a lot of gaming, I would definitely go with a desktop. Really easy to pick your parts and build, not to mention they are extremely easy to upgrade as well.
But if you are just doing a little bit of gaming, laptop would be fine.