According to Steam: 876 Games Owned, 603 DLC Owned. Also have a Desura account with 198 games, but a lot of those are also on Steam. GOG adds another 15 and Origin about 6. Add the games that are on none of those platforms, should be around 1000 games.
Considering Steam is 9 years old now, that's a lot of time to create a nice library.