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.
Crash Bandicoot, Jak and Daxter series, Ratcher and Clank series mostly. Most people usually associate childhood with Nintendo games but they’re super rare in my country, I only ever got around to playing series like Zelda and Mario in the mid-2010s. For what it’s worth the playstation 2 really was the console to have at the time, the games were amazing. Pretty sad Sony is reluctant to make good ports of them for the new generation.
Oh, and everyone I knew had House of the Dead 2 on the computer. Now that’s a classic.