That’s not really DRM, that’s actively providing a service. Some studios try to tie in single player experiences with online components as a form of DRM but those are invariably quickly cracked and are often a source of embarrassing launch day failures so they’re not that common.
That depends a lot on whether or not the servers do actually provide value (e.g. a decent MMORPG – in my life I've played Eve and WoW, until about 2007) or are just egregious (I have a legal license for Adobe's Creative Suite CS6, and I'm sure as hell not upgrading).
