An annoying DRM is always having to be online.
The area I live in gets hit with outages a lot because ISP's are constantly doing line work, Upgrading services etc.... and if the net goes out mid way through a game you then get kicked.
Need For Speed is a good example, Was in the middle of a race recently and even though I picked the option to play on my own without other racers, It still kicked me to the main menu when the net went out.
As Kushiro said, Anno 2070 is another one, I've been bugged by activation screens numerous times even though nothing on my system has changed and I've then been locked out and had to contact Ubisoft customer services.
DRM sucks great dane nadgers.