Who can say? Will GOG? Will Steam? There's no way to tell. If that's your worry, back up your games.
These are subscription services. If a vendor bites the dust, your games are practically lost.(see Direct 2 Drive incident)
You cant possibly back up hundreds, or God forbid, thousands of games.
I have currently backed up 3781 games - all on the same hard drive, neatly ordered into folders. I don't see the problem?
And proof of purchase helps when the police come banging on your door, but otherwise its just there for that warm comforting cozy feeling.
That's correct. Proof of purchase helps _if_ your legitimate ownership is questioned, but not more. However, some publishers _do_ give you access to their game on another service when the service you bought it on has gone under. That's goodwill on their part though, nothing you're entitled to. Every single vendor of digital downloads has a clause in their terms of service that they can't provide the games forever, for good reason.
After the Direct 2 Drive->Gamefly fiasco i only buy game.. subscriptions ;) from digital retailers(or keycodes that can be redeemed in said stores) i feel that will be with us for a loong long time. That means Steam, GamersGate, GoG.. and thats pretty much it.
The video game market is extremely volatile, and the strong players of today might be gone tomorrow, who knows? Direct2Drive looked pretty strong and secure until Steam steamrolled the market. Most of the big players are privately held companies, we simply cannot know how financially healthy they are. Even if a service stays alive, there's no guarantee that you'll be able to use your games in several years - the service might be "upgraded", breaking compatibility with your old games, or support for older games might be cut off because "no one plays them anymore". Expecting that you'll be able to play your games for a long time just because a subscription service seems successful now is a bit naive, imho. If you've followed the business for a few decades, you usually grow a bit more skeptical.
In any case, as others said - the only way to be _sure_ that you can play your games in the far future is to buy versions that are free of DRM, and make backups.