I've given some games away to relatives and friends but I have most of my collection to this day, I never sell my games and I will never buy a used game again either, if for no other reason than not to support an unfair and devious business philosophy that is harming both consumers and developers (I also don't want shitty secondhand wares that malfunction).

I bought my NES in 1987 and have all Nintendo, Sega, Sony, Microsoft etc consoles. I buy 20-50 games every year plus 5-10 handheld games, both new games and used. Never sold any game so my whole basement is full of games and consoles :) It's around 1200 games or something. My favorites among many games are The Legend of Zelda, Super Metroid, Mario 64, Adventures of Lolo, GTA III, Resident Evil. Also love my old ZX Spectrum games like Cookie, Jet Set Willy, Jet Pac, Scuba Dive etc.

22 PS3 games

43 PS2 games

17 PS1 games

12 DS games

3 3DS games

8 Wii games

Too big of a list to name. I still have over 100 nintendo cartridges. But recent games....

32 ps3 games
17 wii games
143 xbox 360 games
7 wii u games.

I'm not even going to try counting. However, the PS3 is the first time I started trading games, mostly at one of the online trading sites, though I have sold a few back to Amazon. If I like it, I keep it, if I don't, I trade it.

I just listed several for trading, actually, because I'm broke and it's the only way I can get more games.

Well you never lose right? Constant morale lift!  Smart smart!

@OP
I have at least  500 "physical" games or so   since I never sold a game. Started with NES and Gameboy.

I also have like 85 games on steam etc.

Too many to mention pretty much all the games in my PS3/360 tag and many, many more.

I usually don't sell games, I haven't done it since early last year. Although I sold like 5-6 games then.
As of right now, I own a handful of games.

3DS -6 games (Will sell one of them)
DS - 8 games, but I have more where my dad lives.
Wii - 8 games, but I have more where my dad lives.
GCN - 6 games
GBA -5 games
N64 - 3 games, but I have more where my dad lives.

I try to keep my library documented

Here's my current list:

Wii U: 6 (+7 Download)
Wii: 33 (+46 Download)
GCN: 5
N64: 7
SNES: 30
3DS: 7 (+41 Download)
DS: 20
GBA: 17
GB: 15
PS3: 7 (+11 Download)
PS2: 8
PS1: 11
PC: 77
iOS/Android: 55 (all download obv.)

That totals to about 400 but as a good portion are downloads and a few I rented or lost and can't find right now the real number is lower. I expect the number to double by the end of this new gen as I will be buying games for 3 consoles actively and want to rebuild more of my older collections (lost quite a few games when my old apartment flooded, had an Atari 2600 and NES with several dozen games and more games for the N64, PS1, SNES, etc.)

Sadly just over 100 of these I've never beat (and about half that never played) so I always have a nice backlog to go through.

I sell games - but only the bad ones.

31 NES
52 SNES
19 N64
6 PSX
9 PS2
11 GCN
1 XBox
49 PS3
7 Xbox 360
5 Wii

40 GB
24 GBA
45 PSP (20 UMD + 25 digital, only counting full games)

12 N-Gage

0 Vita - but I own the console!
2 Wii U

I'm not counting small digital titles like The Walking Dead etc. and also not counting PS+ Titles.