I think a good lot of these series will be from SEGA. When they were in their prime, their games were absolutely amazing. Now, we get Yakuza, which I've heard is quite good, but otherwise their game output seems super lacklustre.
My picks (echoing quite a few others!):
Jet Set Radio
Panzer Dragoon
NiGHTS
Skies of Arcadia
The World Ends With You
Streets of Rage (something like Mania would be fantastic)
We Ski? (bonus nostalgia choice)
Then again, you can't trust SEGA to do much right so I'm not sure...