Hi,
while GoG is pretty much my ideal when it comes to digital distribution, they obviously don't offer any new games. I'd like to try out a few of the other services (my only experience is the Orange Box), but I'm concerned about how they handle game ownership. Do they limit game installation or access in any way? And, very important to me, what happens should they go out of business? I often go back to games I've bought 5 to 15 years ago.
Valve apparently stated that they would in such a case release a patch to make games playable without Steam, but what exactly would that entail? Would I be able to reinstall the game as many times and on as many PCs as I wanted, or does it just mean i would continue to be able to use my old installation?
Thanks in advance for any replies.

Frankly, there is no way to be certain of any of the answers to your questions. In theory, services like Steam could remove the Steam requirement in the event of a business failure, but their own user agreement absolves them from any responsibility to actually do that and since it hasn't actually happened, we have no idea how it might work if they were to do it. Some of them do limit the installs allowed with their games, but it is on a per-game basis, so some will have that limit, others won't. Essentially, it is really up to you to research each game purchase to ensure you don't end up with a really expensive rental that you won't be able to play anymore in 5-10 years.

With Steam, you can download any game you bought from them as many times as you want. It's possible to play the games offline, as long as you check Offline Mode before you go offline. If Steam does go out of business, like you said, they'll patch it so the games are playable without the client. They will likely have a window of time for you to download and back up all of your games before they shut off the servers. If it's done like this, you will most likely be able to download it over and over again to any PC. Something to be said about this is that they don't have to do any of these things, but most likely they will.
Direct2Drive keeps backups of the games you download on their server, so you can re-download as many times as you want. Many of them have limited activations, but a quick chat with their support staff will reinstate all of the activations you had. It's unclear what will happen if they go out of business, since many of their games rely on their servers to authenticate.
Impulse, Direct2Drive, and GamersGate are all extremely similar services. Aside from Steam, my best Customer Support experience has been with Direct2Drive. If there's a game I want that's not available on Steam, I get it from there.
Also, it is unlikely Steam will be going out of business, as it is fast becoming the dominant way to purchase and play PC games.

Steam - Your games are tied to your account. If you lose access to your account you lose all your games. Some games also come with third party DRM such as SecuROM or Tages. Check before you buy.
Impulse - You only need to use your account to buy, download, activate and update. After that you never have to open the Ipulse launcher as all games can be launched from their .exes. Some games gave third party DRM like SecuROM and Tages.
Direct2Drive - No client at all. Buy, download and instal just like a retail CD/DVD game. Again some games have third party DRM.
Gamersgate - No client. Again buy, download, install and watch for DRM.
Gamersgate have the best reputation for customer support. D2D seem pretty decent as well especially when it comes to activations. Steam and Impulse customer support varies from good enough to diabolical.

Not entirely true. You can download and install most games as many times as you want, provided they have not added any third party DRM on top of Steam that limits what you can do.
Also not entirely true. Some games are only allowed to be re-downloaded if you purchased their "extended download service", otherwise you get 30 days to download and that's it.

Oh yeah, forgot about some of those games on Steam.
And for Direct2Drive, I have never had to purchase extended download time from them, and I've bought many games from them. Whenever I go to check out, it's included in the cart, and it's always labeled in big bold letters as free.

"Valve apparently stated that they would in such a case release a patch to make games playable without Steam"
how will you download your games if all Valve content server goes offline?

It's been said before. There is really no danger of anything happening to Steam in the future. Even if Gabe was to go on a waffle rampage and spend the entire Valve payroll then another company would buy the Steam service.

If I were given the reins to a company with that kind of bank, I would do the same, or something equally batshit-crazy.

Wait, what!?
I've bought several games on Steam I haven't bothered to download yet due to lack of hard drive space or intention to play just yet. I had no idea they do this. Do they mark it in big red bold letters or is it in tiny print?
I can't be bothered to download this stuff just to back it up once installed. One of the pluses to buying digital is being able to download them at your leisure.

On the game's Store page, to the right with all the information, there will be a listing if it has DRM.

It doesn't really work that way on Steam, lemme give you a rundown:
Steam - biggest market, tries to remove publishers 3rd party drm, and SALES, SALES UP THE ASS, only place to get valve games
Direct2Drive - pretty good too, activation limits on all games in addition to publisher enforced DRM but easy enough to cutomer support your way through, also pretty good on the sales front but not as insanely good.
Impulse - Steam without all the fun or sales, only place to get stardock games
Gamersgate - Direct2Drive

DRM is one thing, being unable to download after purchase is quite another.
I'll have to check if any of my games fall into that category, though they've been bought and not installed for quite a while now.

Oh you can download them, I thought you were talking about DRM!