Allthough I beleive Shenmue to be the greatest game of all time, I wouldnt say that Shenmue II is better than the first one, as it gets a bit strange towards the end, (I wont spoil it for you!) but its still a fantastic game, a worthy addition to your DC collection, and will leave you wanting more!
but the DC version is Japanese/English subtitled.
Games you must own are:
Jet Set Radio
Sonic Adventure
Crazy Taxi
Virtua Tennis
Soul Calibur
Shenmue & 2
Metropolis Street Racer
Trickstyle
Toy Commander
House of the Dead 2 (Using the light gun)
Daytona USA 2001
Sega Rally
Space Channel 5
Ecco
Virtua Fighter 3tb
Phantasy star online
...where do I end
oh, and a few strange games worth a try:
Seaman (Strange virtual pet game which you can talk to using sipplied mic, very strange how well it actually works, and strangely addictive, US released only but it works with a boot disc on a PAL DC)
Sega Bass fishing (if you drink alcohol a lot (like me), using this game with the official Dreamcast fishing rod, with a few drunken mates is a great laugh)
Occasionally you will find most of these games available on EBay brand new, still sealed, so go and get em while you still can.
EDIT:
Oh, and Dastardly, you can now add the wonderfull Dreamcast to your Biography, lol