Welcome to DC-Talk! You know, Adam was also one of the reasons I bought a Dreamcast.
Here are some recommendations:
Sonic Adventure: Get this if you want a good and fast 3D platformer. The cutscene graphics haven't aged very well, and that's one of the reasons why people like SA2 more. Personally, I prefer the first. I mean, who doesn't love running around as a small blue hedgehog in city streets?
SoulCalibur: One of the big ones at launch. A Namco fighting game where the graphics are so realistic that they surpass the arcade version! Wowza!
Spirit of Speed 1937: Just kidding. Avoid this one as much as possible.
Literally.Power Stone: Great fighting game from Capcom. With Power Stone 2, they made it so 4 people could play at once, ala Super Smash Bros. Sweet!
Resident Evil: CODE: Veronica: One of the greatest RE games of all time. And I'm pretty sure everyone can agree with me that it's better than RE 2 on the Game.com.
Seaman: An interesting game...you talk to a fish with a human face. At first, it learns language from you until he is able to fully interact with you. It's quite amazing that they had this technology in 2000. Speaking of having advanced technology in 2000...
Phantasy Star Online: One of the very first online RPGs ever made. In fact, you can still find people playing online with this game on private servers (ex.: Sylverant).
Shenmue: I'd probably get slapped in the cheek ala Three Stooges if I didn't mention this one. If your friends say that PS2 looks better than Dreamcast, get out that VGA Box and show them
THIS.