At first a person simply doesn't notice.
Then a person starts to do it through their superior memory like a Jedi.
Not long after that starts to fail we revert to Spreadsheets.
Finally we give up and just pretend we like things twisted, the spreadsheets get recycled to keep track of the millions of User-names we end up having with all the various distributors of Game Keys.

Me too, several hundred. I have an exceptional memory is all, I realize this. It's probably from doing lots of memory exercises through life.

I have a second word: "brain" :P

Well that is always useful...though I remember having a better memory ;-p

I apparently don't keep them straight. On at least two separate occasions, I've traded for games i already owned.

I've tried the spreadsheet method, but inevitably, if I buy a game out bundle while on my phone, I forget to update the spreadsheet, despite the fact that my spreadsheet is in Google docs. Then I've got a spreadsheet that i don't trust.

for me it's easy, GOG doesn't have the game I have on Steam

I don't use any other platform except gog.
and on gog i'm only buying exactly what i want and i'm interested at, not titles considered (by me) bloatware.
so it's easy

I only have few hundred games so that is not really a problem for me as I remember each game I bought. I do have few repeats but each was bought second time on purpose.

Unfortunately I don't have much. Every time I started a list it ended up unused after a while. The only lists I have which are up to date are the games I own on bundles from Groupees, Indie Royale and Indie Gala, and those are kept in gmail drafts. I've been wanting to create a Google spreadsheet with an extended UI for a while, but I never get to it.

Easy, try finishing your GoG collection first before trying other collection.

Once you realize that you probably cannot finish your GoG catalog in your lifetime, you have little motivation to manage your steam inventories anymore

I don't bother with lists. My main store is GOG and I only buy from other stores if GOG doesn't have something that I want, e.g. Heretic, MegaDrive Collection or Titan Quest to name some of them. Thus, it's easy to remember if I already have a game from one store.

Added to first post:

Edit because people seem to be missing the point: I HAVE SIGNIFICANT COLLECTIONS ON BOTH PLATFORMS. It's all very well to have snide comments about DRM-free gaming and how superior you are by not using steam, but THIS IS NOT THAT THREAD. This is a thread about how people with large game inventories across MULTIPLE platforms keep track of them.

On my computer I have separate folders eg:Steam,Gog,Origin,and so forth.When I go to a different site and can't remember whether I have that game or not.I just look on my quick launch setup in the folder for the game,which takes a matter of seconds.Maybe this will help you..

I have significant collections (+-700 each) on both platforms. How do I keep track of each? Well, steam for AAA games, and some oldies and indies from before I made the full GOG switch. On GOG, basically everything else, I need to filter out which games I consider candidates for playing and I let GOG curation do just that. I have also often re-bought games I owned from steam on GOG, as I like having a hard disk with my game collection and steam doesn't let me do that; I never buy a game on steam if it's available in GOG (unless it comes in a bundle).

This is how I manage my game inventories among MULTIPLE platforms and how I keep track of them. If you don't like it or think I act superior through snide DRM-free comments, well, tough. That's your problem, don't ask a question if you don't want to hear an answer you don't like.

I use a spreadsheet. The first column is the title of the game, and the other columns represent different services (GOG, Steam, Shinyloot, Humble etc). I just put an x if I have the game on some service.
I also tend to have lots of doubles, like right now I re-bought many Nordic games here..