I usually get rid of most of my games as time goes on. Once I decide I'll never play it again, I sell it. Like TIE Fighter and Xwing and Star Trek Aramada. Stupid me!
Some I keep, though. But none of the ancient old ones I once had. Gone are all of the C64 and Atari. Gone are the NES and Sega. Gone are most of the XBOX titles, even.
I think it would be Hardwar (1998). And I actually had to re-buy it b/c I got rid of it ages ago. That was a weird game. I bought it at EBGames for 1 cent. They were giving them away. They said it sucked. I loved it. I was completely engrossed, played it death, then put it away. I got rid of it around 2002 or so. And then a strange resurgence came up and tons of people were playing it -- often networking together. I missed that heyday and only read about it on the Internets. But I ended up getting it again after talking to someone on GOG who said it worked fine and had an HD patch.
I have older games on disc, but they are newer bundles (for example, I had BG1 and BG2 w/o the expansions -- it was cheaper to just buy the $20 collection on DVD back in the day).
I like getting rid of games. It makes me feel good. Someone else can play them. And that's great. But there's a few I sorely miss. Most of which, however, I now own on GOG.