1) Unbeatable Enemies
In Serious Sam 3: BFE, the game developers inserted a giant pink scorpion that forever haunts the player until he dies. Not only that, but they blessed the creature with super speeds and immortality. :P (Warning: the video has lots of digital blood.)
In EarthBound, it actually lets you go through the entire game, and then crashes during the last boss fight and deletes all your saves. O_O
2) Broken Controls
This category seems to be fairly popular. In Crysis: Warhead, your weapons not only become fairly inaccurate, but also your ammunition supply magically turns into chicken.
Mirror's Edge is a game all about free running, so what happens if you lose the ability to run?
Grand Theft Auto 4 not only cuts the brakes to all your cars, but it even starts messing with the visuals so that you feel like you're playing drunk (the fun starts after minute 3:11).
Piraters of Batman: Arkham Asylum soon discovered you no longer have the ability to glide. I love this quote from the Eidos forum administrator: "It's not a bug in the game's code, it's a bug in your moral code." :)
3) Destruction of Everything
The creators of Maniac Mansion inserted a humorous warning sign in the game, and then proceeded to destroy you and the entire mansion via a weapon of mass destruction.
Developers will always try to outwit piraters in this never-ending war, but still, it's funny to see how many clever ways they can say "we caught you." :)
Invincible Killer Scorpions And Other DRM Hijinks
Escapist Forum Post: Funny DRM methods for any game