Quote from GOG FAQ:
"Yes. We do not limit the number of installations or reinstallations, as long as you install your purchased games on computers in your household."

I guess in my mind something can be all those things and still be "classic"!

Always interesting to see someone ask a pretty simple straight forward question and then see all kinds of orthogonal discussion fire off in different unrelated directions from there with people Internet outraging against each other for no real purpose or gain for themselves nor the community as a whole.

All that over a simple question that can be answered simply with "yes" too. It's very sad to see the community here going down this path against each other.

Can't really help it. The answer is indeed a simple 'yes,' but since Windows 10 is mentioned, let's veer off the original path and talk about how Windows 10 sucks or something.

Truth of the matter however, is that yes, you can download your games again, on any system that pleases you for any system. Downloading a game to a Windows 2000 machine is more than possible, and you'll still obtain that Mac OS version of the game you're eyeing. The same is true for any other operating system that can connect to the internet.

Easy answer = Yes. You can in fact install your games on several computers.

Download? Yes

Actually play? Not so sure.

Better off resetting the computer to Windows 7 or XP. But that's just my opinions. Oh and if you do, turn off Automatic Updates, as it's a shitstorn trying to push Windows 10 at you regardless of what you prefer.

All my games that worked previously, work now. I'm on Windows 10.

The only strange things I've encountered is, in games below DirectX 9, some game's brightness options no longer work. Also, sometimes a game will just hang out in the task manager without actually launching. Just go to the game's folder and either rename the "winmm.dll" to "winmm.dll.bak", or replace it with one from a game that has it and launches fine.

So yeah, down rate me all you want, Windows 10 so far feels like a less restrictive Windows 8. I using a local account, shut off all the bullshit, and any games that give me trouble, I've found solutions either here, the PC Gaming wiki, Steam community and sometimes the VOGONS forums. I know some people had pretty bad experiences with 10 early on though. But in general and game wise for me, so far so good.

I hear quite different things for what MS wants... with games as apps from their store with UWP, it would be more restrictive, as bad as or worse than GFWL.

I heavily caution against Windows 10, until this is fixed.

You're speaking about a very tiny selection of games owned by Microsoft, and UWP isn't going to get anywhere. Much like GFWL it will fall on its face and slowly rot away because nobody is going to fall for the same shit twice. Have you seen the general consensus PC gamers have with MS? I wouldn't exactly call it friendly and inviting.

I'm talking about the entirety of my Steam and GOG library. I'd say 90% of my games so far work with no tweaking, 5% needed tweaking and then ran fine, and the last 5% don't work as well as they may have previously. Some of those cases I suspect are actually driver related as well, not so much OS related.

I'll go against the consensus here and say:

No, you can't.

I'm a rebel.

Well, I will ignore the Windows part as that is not relevant. Yes you can download your games anytime you want whilst the website is available. This is the point, your reliant on the website being available. I still don't understand why people rely on these things. Backup your product so its always in your control, save the files to an external HDD. Me personally I have four rotating backup drives, and am looking to improve that by adding a RAID server. One day you will switch on your computer and nothing will happen, it will you know, or GOG will disappear, or the web will go, and at that point you will think, why didn't I backup all my stuff offline under my control, now I have lost everything. Backup, then backup again, and if its a weekday ending in Y backup again.

TL;DR; Backup, backup, backup, repeat ad initium.

Example:
https://www.gog.com/forum/general/shinyloot_plans_for_dormancy_in_2016

Backup!

Awesome, I enjoy seeing that not everyone goes with the flow and accepts the majority rule.

Bigfella007, now you have all the answers you may wish for:)

Yes you can download your games again.

That's the most accurate answer to your question.