These could be games that left a lasting impression on you, games that had stellar gameplay mechanics, characters that captivated you, games that you played tons of hours on, etc.
When I was a kid I used to walk to the movie store to rent games. I would go back every time I had money and rent Chrono Trigger, but some one would always erase my save, so I would have to start over.
On my birthday I got a check from my grandma that was for 50 dollars. I walked right up to the game store and slammed my check on the counter for one copy of Chrono Trigger. I didn't know how money, checks, or sales tax worked.
Luckily, my mom bailed me out. I played that game for years. I still have such fond memories of that game.
It's amazing that CT never spawned an ongoing franchise. Aside from the controversial CC, there have been no other followups or even remakes, only a remaster. It's like the platonic ideal of a JRPG, sitting alone and unsullied in the timestream.