Every airline has at least slightly different policies, some are vastly different. You'd be best served looking in specific airline forums for any sticky FAQ threads.

AA and UA require some form of purchase, miles or instrument (500-milers, SWU's) for an upgrade. Though it happens, it's generally not assumed that an elite traveler with receive an upgrade on these airlines without these or some other reason.

DL, CO and US all provide complimentary upgrades to elites. Not exactly sure how DL and CO work on timing but US works like this: On North American flights only, provided the proper inventory is available, elites are upgraded automatically at the 7, 4, 3 or 2 day windows depending on status level. A single companion is upgraded at the same time if two seats are available, otherwise I believe they are skipped over. Also, members with more than one companion are not automatically upgraded.