Sega had very good relationships with third parties by the time of the Dreamcast. They got strong support from Capcom, who developed their next Resident Evil game for it (that's huge. It later got ports of RE2 and 3) also Street Fighter 3rd Strike was a first for a console, and was the cradle of many other new Capcom franchises like SNK vs Capcom, Power Stone, etc. A new 3D Castlevania was in the works from Konami but got trashed when the console didn't take off. It got Soul Calibur from Namco, which had been practically married to Sony, that's says a lot too. It also got reknown non-japanese franchises such as Tony Hawk Pro Skater, Quake, Unreal Tournament, Rainbow Six, Rayman etc.
And look at the scores (but notice there are many good games missing here, and many bad ones as well -for example, Rayman 2 , Sword of the Berserk and MDK are missing, to name a few- )
http://www.metacritic.com/games/dreamcast/scores/
Look at the years. Basically, in two years (2000, 2001 - the DC was released at the end of 99) the DC had more 90+ games than Xbox 360 (which is in its 3rd year since November 07) Wii (it has 5 in a year and a half) PS3 (which currently only has 4, after 1.5 years) You may present arguments saying the quality of the current generation AAA is higher, or the reviews for Wii don't count 'cause the reviewers are biased against it, or probably those Metacritic averages result so high beacuse not so many reviews are taken into account compared to this generation averages. Whatever the reason, and this is 8 years ago we're talking about, the message here and undisputable truth is this : The Dreamcast had a hell of a great library, specially being so young. It was that good when the PS2 was released with a lackluster lineup which didn't improve after several months in the market.
As a poster above mentioned, the PS2 had DVD, that was a great factor yes, but the PS2 was also the successor of the PS1, the heir to the King with the likes of Electronic Arts by its side and Square-Enix and many others. The PS2 plays PS1 games, it's compatible with PS1 controllers and memory cards too. Just as PS2 was (and is still) very strong after Xbox 360 launched, so was the PS1 when the DC released, people bought it at first, but not enough, Sony PS1 was cheaper and had tons of great games and the PS2 promise was very near. The DC didn't get a real KILLER APP as the likes of Gears of War (Soul Calibur was a great start, but the DC never got anything as popular after it) And then there's the PS2 price, next to all the points in its favor, it also was "cheap" compared to the inferior DC (only a $100 or so difference, you were getting a DVD player and a PSone too) Sega was badly hurt financially after the Saturn and they just couldn't take more losses. The Dreamcast was heavily pirated too, which made things worse. I don't doubt if they had chosen DVD as its format they could've even launched a little later, evade piracy a lot better for a longer while and, who knows, they could have found a niche in Europe/Japan and stay profitable for a whole generation. I guess the dream was not meant to become reality....