I happen to be curious about a genre that I tend not to play, and for which I do not own any games from this site: namely abstract puzzle games.

Here is what I mean:
* The game must be a puzzle game. This, in particular, that there must be consistent rules the game follows (i.e. 3 of the same in a row makes them disappear).
* It must be abstract. In other words, the game play should not involve controlling a character or similar things.

Famous examples of this type of game include Tetris and Bejeweled, to give you an idea of the type of game I am looking for here.

Spacechem.

How does this make it an "abstract" puzzle game? What you're describing sounds just like a regular "puzzle" game.

There's not really all that many on this place except for Spacechem, Infinifactory, Sokobond, and MechoEcho, unless you're going to count strategy games.

TIS-100 might count, but I'm not sure if it can really be called a "puzzle" game. Not sure what to call it, really, it's pure programming.

I'd personally throw in Fract OSC, Myst, The Witness, Where Is My Heart, and possibly Human Resource Machine, but these seem to break your "rules" a bit.

This. Ridiculously challenging at later levels but loads of fun, and probably on sale for about £0.69 right now (it usually is during the big sales)

Sokobond isn't bad either.

And Mini Metro is a lot of fun (well the demo I played was, haven't got the full game yet)

Ah, that one slipped my mind.

I'm rather saddened that there aren't more puzzle games on here. I'd really love to see some basic timewasters like Prismatica or Hexcells.
Or, to keep with the whole "old games" thing, maybe some of the PopCap games.
Edit: Wait, I forgot EA bought out PopCap. Nevermind, that ain't gonna happen until the day Barry sprouts wings and flies.

Just give him Red Bull, according to the commercials that problem is easily solved.

Highly recommend the Hexcells games, each games builds on the mechanics of the previous one and adds some stuff.
Just play them in order as each ramps up more quickly in difficulty.

?

As opposed to games in which you assume the role of an actual person who manipulates the environment to solve puzzles, e.g. Magrunner, qube and the like?

Wait, are you looking for block-matching games or do you want puzzle games? Because if you want block-matching games, I can't really think of any on Gog. If you're looking for puzzle games, TIS-100 might be up your alley.

I suppose Pony Island might qualify, at least from what I've seen of it.

I would look at HuniePop, it fits your "3 of the same in a row makes them disappear" rule. Another is MouseCraft but both of these you do play as a character. Sounds like you want a puzzle game without a story just puzzles and those are difficult to find.

Triple Town should fit the bill.

Even in Spacechem and Human Resource Machine you play a character. The character in question is just not visible on the screen.

I always forget that one is on here. It's a nice little game (played it on mobile years ago), and the guy (or one of the guys) who made it also maintains this website:

http://www.lostgarden.com/search/label/free%20game%20graphics

Which has loads of great stuff and free to use graphics for games, so a developer well worth supporting :)

So, you are after something in the casual puzzle genre? You won't find much of this on gog, since many Gamers would feel that it rub them the wrong way.

On this platform, Triple Town and Unholy Heights fits the bill, but I couldn't really get into them.

While it IS a shooter, Crimzon Clover: World Edition has the same hectic and brainless flow as a good match-3.

I would recommend looking at some titles from PopCap - Plants VS Zombies, Peggle Nights, Zuma .. not all of them are abstract, but they have the same feel.

10,000,000 is a combination of match-3 gameplay and dungeoncrawl. Quite good, but you have to divert your attention between the dungeon and the playfield, and while you only interact with the latter, this is still a bit confusing. Not bad, though. I think it even count as roguelike.

I remember I once played a really good Match-3 game with RPG-ish powerups and story. Can't remember the name, though.