There were only about 400 games released for it in the US but I wouldn't be surprised if it had the highest average game rating of any console ever built. Basically there werne't many games but the few that it did have were amazing.
What games you get really depends on your tastes
The Dreamcast was pretty much my only console between the PS1 and the Xbox so it got a lot of play. I still play it all the friggin time

If I had to pick one console for the rest of my life it would probably be the Dreamcast.
Here are some of my favorites from various genres...
RPG:
Armada
Grandia II
Phantasy Star Online
Phantasy Star Online Version 2
Record of Lodoss War
Shenmue
Shenmue II (only released in europe and japan)
Skies of Arcadia
FPS:
Halflife
Outtrigger
Quake III Arena
Unreal Tournament
Shooters:
Bangai-O
Cannon Spike
Gunbird 2
Mars Matrix
Silent Scope
Action:
Alien Front Online
Gauntlet Legends
Headhunter
Jet Grind Radio (prequel to Jet Set Radio Future)
Legacy of Kain: Soul Reaver (the best game of the series)
MDK2
Resident Evil 2
Resident Evil 3: Nemesis
Resident Evil Code Veronica
3D fighters:
Soul Calibur
Dead or Alive 2 (There's a slightly better Japanese LE version)
Fire Pro Wrestling D
Project Justice
Ready 2 Rumble Boxing (cartoony 3D boxing but very fun)
Ready 2 Rumble Boxing Round 2
Ultimate Fighting Championship
Virtua Fighter 3tb
2d fighter:
Capcom vs. SNK: Millennium Fight 2000
Fatal Fury: Mark of the Wolves
Guilty Gear X
JoJo's Bizarre Adventures
King of Fighters '99: Evolution
King of Fighters Dream Match '99
Last Blade 2: Heat of the Samurai
Last Blade 2: Final Edition
Marvel Vs. Capcom: Clash of Super Heroes
Marvel Vs Capcom 2: New Age of Heroes
Street Fighter Alpha 3
Street Fighter III: Double Impact
Action/Fighters:
Ooga Booga (kind of like Smash Bros)
Power Stone
Power Stone 2
Tech Romancer
Virtual On: Oratorio Tangram
Racing:
Crazy Taxi
Crazy Taxi 2
Daytona USA 2001
Ferrari F355 Challenge (one of the most realistic racing sims ever)
Hydro Thunder
Metropolis Street Racer (prequel to Project Gotham Racing)
Re-Volt
San Francisco Rush 2049 (the multiplayer battle and stunt modes are fun as hell)
Sega GT
Sega Rally 2: Sega Rally Championship
Test Drive Le-mans
Test Drive V-Rally
Tokyo Xtreme Racer
Tokyo Xtreme Racer 2
Vanishing Point
Platformers
Rayman 2: The Great Escape
Sonic Adventure
Sonic Adventure 2
Puzzle Games:
Bomberman Online
Bust-A-Move 4
Chu Chu Rocket
Wetrix+
Worms Armageddon
Worms World Party
Music Games:
DDR 2
DDR House Edition
Samba De Amigo (think DDR or jungle beat but with maracas)
Space Channel 5
Space Channel 5 Part 2 (Japanese only release)
Rez (One of the coolest games ever made, Japanese/Europe only release)
Other:
Confidential Mission (gun game)
House of the Dead 2 (gun game)
Jet Coaster Dream 2 (design and ride your own rolercoasters)
Seaman (uh... you'd have to play it)
Toy Commander
Typing of the Dead (House of the dead 2... teaches typing)
Sega Bass Fishing
All Dreamcasts made before December of 2000 can play backups with the Utopia Boot disc, or with the boot disc built into the game disc to make a "self boot" game. Consoles made after December of 2000 need a modchip (they're hard to find but they only go for about $10 and it's 4 easy wires). Despite that I've never EVER found a Dreamcast made after Dec of 2000 in the US. I think only the last round of Special Edition Japanese consoles were... Though if you go with the modchip you wont need a boot disc or self boot games at all.
EDIT: Almost forgot
The DC also had a number of really cool controllers and add ons
-VMUs: instead of memory cards it had "VMU"s which looked like a miniture gameboy and lots of games had mini games you could download to it, you could also transfer save games from VMU to VMU without a console... In game the screen would be used to do things like show your health in Resident Evil or in a card game it would show your hand, or a your Football play etc... it was very useful and I whish newer consoles had something like this.
-Shaker Packs: like the N64 the rumble feature came in the forum of a plug in Shaker pack. (the DC controller had 2 slots so you could hold a shaker and a VMU in one controller)
-Lightguns: there were 4 light gun games for the DC, House of the Dead 2, and Confidential Mission, were the best, there were 2 more Japanese games that were ok. The Lightguns had a port on the back for a shaker pack that would kick the controller when you fired, or you could use a VMU and it would display your ammo
-Fishing controller: Motion sensors for casting and pulling, just like the Revolution commercial... it's even got an analog reel. Not just good for fishing, it also works well as a one handed RPG controller...
-Arcade Joystick: the Dreamcast controler had a 4 button diamond layout and 2 triggers, not too good for fighting games that required 6 buttons (triggers suck for fighters), Sega had an official Joystick made by Agetech with 6 arcade quality buttons, and most fighters recognized the stick and would relable the controller configs accordingly! I had 2 of them and loved them to death (sold them both though).
-Twin sticks: the only way to play Virtual On (if you've ever seen virtual on, cyber sled, or WAR in the arcade... those are twin sticks)
-Maracas: a pair of analog maracas for playing Samba De Amigo
-Keyboard and Mouse: 2 separate controllers actually but AFAIK all FPS games supported them. The keyboard could be used for games like typing of the dead or Phantasy star online or just entering text for most games that supported it. The DC also had a web browser so you could use these for that too. A few other games also supported the mouse (Rez is the only one I can think of but there are more)
-Dance Pads: because every console needs dance pads
- Broadband adapter: from the factory the DC had a modem adapter, but there was also a broadband adapter... if you can find one BUY IT, I don't care if you don't even own a DC, they're worth upwards of $100 if it's working.
-Microphone: the main method of control in Seaman, also used for voice commands in games like Alien Front Online.
-Racing wheel: The only thing better than Analog triggers
I'm sure I'm missing something to...