Mass Effect uses SecuROM. The draconian parts were removed because of an onslaught of emails from players saying they would purposely not buy the game and would pirate it if they pursued it. Bioware backed down and now the game only checks CD keys during downloads of extra online content. This is fine by me but nasty SecuROM is still on my system and is still using bad registry keys to keep me from removing it. Also they now detect some SysInternals software that will help you remove bad keys and will thwart it's attempts and/or make your game unplayable if you have it installed.
But certainly, I do think there can be a non-intrusive copyright protection, and Mass Effect is a step in the right direction. It's not quite there yet, but I think it will be less to complain about rather than SecuROM or Starforce.