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.
I've got a really fond spot in my heart for The Neverhood. It really opened my young eyes to the possibility that video games could be weird and artistic. They didn't have to be an action packed generic mainstream capitalization of whatever is popular at the moment. As a kid, I could still tell it was a unique piece of work that required a lot of passion and creativity. I consider it the first indie game I ever played and it absolutely set the tone for what I chose to play to this day.
I still listen to the soundtrack nearly three decades later.