About maybe 1000 games.

I stare at the backlog and the backlog stares back.

backlog never heard of this
(jumps under the bed as angry hd's and boxes starts to protest)

GOG alone it is over 200 games.
With everything more like ~400, but lots of those are indie game I hope should be finished in about a week each.

If I add just one more game to my backlog it will collapse into a black hole.

I assume it's over a hundred games on my end, but I'm not entirely sure.

Short answer: A Lot.

My count makes it 42, excluding those games (eg Amnesia) which I got as part of bundles and have no intention of playing, ever.

Over 10k

I plan to have my brain uploaded into a computer and have that computer also include emulators capable of running the games. Then I'll have all eternity to play them.

I can't say. I decided not to care about. What I know is that I generally start lots of games and actually only finish the ones who kept my attention long enough. It can vary: one day, that game won't last long, in a few months I won't be able to stop playing it.

Currently, I'm playing a lot (really A LOT) of Might and Magic VI and Dust: an elysian tale. Man, that one, I only put one hour into so far but it's very very promising. And Might and Magic VI, well, that's an old friend I never managed to finish, but this time, I think I might be able to go to the end!

Ha! I beat you all! (If we're judging by Backloggery alone.) http://backloggery.com/f5inator
...Now I feel sad. But at least by backlog is colorful like cotton candy. 8-3

Embarrassingly big.
You've even beat me I think! I have neglected my backloggery for a couple of months though so it doesn't reflect the true total. Doubt I've bought 200 games in that time though.

There was a point in my life when I wanted to play all the games. That made me buy a lot of titles I was not even remotely interested it. I guess my backlog is pretty big thanks to that.