The problem with most DRM is that they may use rootkits. While I don't believe DRM software like SecuROM will damage your hardware, malware can employ similar installation and cloaking techniques. People don't like software being installed on their computers without their permission, especially software that is difficult to detect and more difficult to remove.
Simple optical disc DRM is tame, this type isn't used anymore. Most people hate activation-limited DRM which employs low-level edits to keep track of software activation status. Bioshock initially had a 3 activation limit AFAIK. Also certain software has to be deactivated before it can be transferred to another computer or installed again (even on the same computer). Adobe Photoshop CS uses this method.
DRM technically isn't malware, but to some it might as well be malware.
Certain anti-virus applications (Norton's) are infamous for employs similar functions. This is why certain versions of Norton's need a special uninstaller.