i wonder that nobody did mention Einhander for PS1 already? or did i read too fast? but you won't get this gem of a game cheap today because it was only sold in japan and USA and today it's very rare. glad that i still own it. others: every Ridge Racer/Rage Racer, every Wipeout, Soul Edge aka Soul Blade, every Biohazard aka Resident Evil, Air Combat/Ace Combat. edit: forgot to add Final Fantasy VII/VIII/IX, Gran Turismo 1 & 2.
for my opinion Virtua Fighter 3tb and Sega Rally 2 were bad parts on the DC compared to the model 3 originals but VF 3tb was a much better conversion than SR 2 and could be worth a look because it's cheap to get.
other good games where Headhunter, Shotuko Battle 1/2 (aka Tokyo Extreme Racer 1/2), Metropolis Street Racer, Shenmue I & II (expensive, rare), Soul Calibur, Dead or Alive 2 (both fighting games are far ahead in positive ways -fun and technical- from VF 3tb), Airforce Delta (aka Deadly Skies), Power Stone, Marvel vs Capcom I/II, House of Dead 2, Biohazard CV aka Resident Evil: Code Veronica, Sonic Adventure 1 & 2, Daytona USA 2001 and there's except of both Shenmue's another rare, expensive gamte to collect: Skies of Arcadia, one of the last great SEGA games - great japanese style RPG. edit: added SEGA GT (Gran Turismo contender, but has not the quality GT has in fact of car controls but makes also fun to play. the european version has more car manufacturers and of course cars then), Le Mans 24h from Infogrames, another great racing game and in my opinion it has the best graphics for a car racer on DC. also Killer Loop was a great Wipeout rival and was made good. i also forgot to mention Crazy Taxi 1 & 2.