I'm sure that somewhere out there there's a person or group that would love to keep servers running for just about any online game that's ever been released, but I imagine that the companies that own the rights to the game won't let that happen in all but a few cases.

Aside from that, I have a feeling that, while we will move more and more towards "games exist[ing] exclusively in the cloud, wrapped in increasingly-impenetrable DRM and requiring networks of authenticated servers", we'll also have more and more gamers pushing back against it. Whether it be in the form of pressure to maintain physical media for storage or simple emulators, for some games, I think we'll start to see the gaming crowd at large push back against an industry that seems to want to only allow gamers to play a game for a short time before it reaches a state of (planned) obsolescence in order to guarantee they can sell us the new games year after year.