Marshalljim890: Achievement support.
Hello and welcome. Please don't feed the inmates, they need a special diet, and giving food (even for thought) at random might yield unpredictable results...
As to your question: As Ice_Mage wrote quite a few games support achievements, if you run them through the local launcher (Galaxy).
However the main point of GOG is that the launcher is optional. You can download offline installers of your game, turn your back and never log in here again, and your games still work.
Personally I don't care for achievements much - for me games are about story, atmosphere, escapism, and some popup telling me I killed 15 enemies with their own grenades frankly only distracts from that. I also don't buy any game that
requires me to use a launcher to play it - I want my games working even if the internet goes down and/or when all the authentication server have turned to dust. For me games are like books - you pick one of the shelf of the collection you own, and no third party has a say in that. And hope my children, grand-children and grand²-children can do the same and maybe understand what the old man was so excited about.
But that's just me. If you want to have full achievement support on all games and don't care about ownership the being forced into using clients, Steam is probably the better choice for a lot of games. If you want to use only one launcher, one unified library, Galaxy can still do that (it launches Steam in the background for games from that place).
On the other hand you can manually add GOG games to Steam - but those won't support achievements, even if the GOG version has them.