I've played many games and there's a lot I really like but I'm only going to list my top 3 in the order of release date.
Sonic Adventure
This is the first game I played on the Dreamcast. I really fell in love with the story, gameplay and music. It truly had an adventure feel to it. Seeing Sonic turn Super Sonic to fight Chaos was so cool. I also liked the character Tikal and wish she would play a more important role in a future Sonic game. Sonic Adventure is what really made me become a fan of the Sonic franchise and I think this is true for a lot of Sonic fans.
Sonic Adventure 2
I really liked the introduction of the new characters Shadow and Rouge. Like the previous game, the music was really cool. I enjoyed most of the levels except for the spooky ones. Something about SA2 felt off for me though, I'm not too sure what it is but I didn't get the 'adventure' vibe that I got from SA1. I think it's because in SA1 there was more moving about throughout the maps, like how you would go from Station Square to Mystic Ruins etc but like I said I'm not too sure why I didn't get the same vibe from SA2.
Sonic Heroes
When I first got Sonic Heroes for the original Xbox I fell in love with it almost immediately. The intro touched my heart. The location where Sonic, Tails and Knuckles were running through was beautiful and the music was so cool. But what really got me is the friendship that was shown between the characters within each Team. Like when Sonic grabs the arm of Tails and Knuckles, it was so lovely. The look on Knuckles face makes me laugh. It's scenes like this that I really love because there's nothing better than friendship and helping one another, and on top of this, going on an adventure together. If you don't know what I'm talking about you can watch the intro here,
https://youtu.be/veUwUdBuTwA?t=50 (it begins at 50 secs). The entire intro gave me an adventure vibe. I'm not talking about the previous Adventure games. I mean the actual definition of adventure. I also loved all the ocean stages in Sonic Heroes, like Sea Gate, Seaside Hill and Ocean Palace. Anyway, I think it was also around this time that I started to become part of online Sonic forums.