On Steam I have a total of 71 games, 34 of which are installed, which includes a few F2P games as well. But if I count every single games I own on other digital platforms (GamersGate, Origin, et cetera), as well the my physical copies of PC and consoles games then I think I'd get a number within the 350+ or so. I actually need to count them... I haven't checked that since a few years. I'm not even sure if some of my older consoles still work, I haven't touched my Turbo Gxf-16 in two or three years.
And, side note, I actually don't have enough HDD space to install all of my PC games. I will upgrade my HDD eventually, since I do want to install all of them for the heck of it, at some point.