Although I was more of a collector in the Dreamcast heyday and had some of the rare hardware and software, the first "killer app" title that stands out is Rez. I think it was only released for the European Dreamcast, so to play it on a North American unit, you had to have a modchip. I also got Shenmue II, which was only an "XBOX exclusive" if you didn't have the means to play it on a European Dreamcast.
Other games that stand out are:
Ecco the Dolphin - beautiful soundtrack, and the first game in ages that impressed me with its graphics.
The Typing of the Dead - grab two keyboards, and you'll be surprised how much fun this can be at parties. The Tutorial mode is probably better than Mavis Beacon.
Sonic Shuffle - despite a couple flaws, I like that it improves on Mario Party by using cards, which adds strategy over just rolling dice, and also puts the VMU displays to use. I also like that it doesn't automatically slam all the players with a minigame after every turn.
Power Stone (2) - Capcom's answer to Super Smash Bros. It also includes a trio of minigames that you can play on your detached VMU, so get yourself some CMOS batteries.
Mr. Driller - just when you thought modern games had to be complex anymore, along comes something simple and fun.
Crazy Taxi (2) - anybody who compiles a list of best Dreamcast games and leaves this out is asleep at the wheel, pun not intended. It's even more fun at parties if you have a steering wheel accessory.
Chu Chu Rocket - good use of multiplayer.
Samba de Amigo - obviously you had to be a hardcore collector to have one set of maracas, let alone two. But anything that draws a crowd at parties is definitely a winner.
Capcom vs. SNK - one of the last games to put to use that cable to connect the Dreamcast to a Neo Geo Pocket Color, and fun in its own right.
Sonic Adventure - Sega's first serious effort to make Sonic relevant again after the original trilogy. It had a lot of add-ons that you could download. I liked the Christmas Tree that would change the music to the a cappella remix from Christmas Nights.
Skies of Arcadia - My wife loved it and played it most of the way through. By now I'd gotten annoyed with RPGs with turn-based combat.
Quake 3 Arena - just as good as the PC version at the time, and you could play with a keyboard, mouse, VGA cable, and Broadband Adaptor, so it might as well have been a PC. That was the problem: playing against PC users meant you were the only one who couldn't have mods/cheats.
Propellor Arena - another fantastic multiplayer game. Sega finished it and then decided not to release it because 9/11 had just happened.
Half Life - rumor has it that it wasn't released because it was better than the Playstation 2 version. Probably the best reason to get a keyboard and mouse for the Dreamcast.