Edit: I'm a dumbass and forgot to mention the game I've easily played the most over the years: RuneScape 2 and currently Old School RuneScape. I love it. Lol
The biggest game for me in my childhood was Starcraft: Brood War. It got me into super RTS games, and even though I played it on the Nintendo 64 (which sucked in retrospect lol) it was the first game I really got into.
The next two games that come to mind were Super Smash Bros and Halo (specifically 2, but really all of the ones before 4 I played a ton of) just because these games were super easy and fun to play with friends and family.
And there were some honorable mentions like Phantasy Star Online: Episodes I & II and Star Wars: Knights of the Old Republic 1 & 2 and Star Fox 64, since these were also games that I played a ton of.