I think it was during there Dreamcast days....but I missed out on Saturn so I guess I could be wrong.
Too broad of a question and too long of a history. I would say the taikan arcade series was the most ahead of it's time and had a lasting impact. The last time they showed true arcade innovation which rubbed off on the industry was probably VF.net
Actually that was planned at one point for the saturn and there was even a script for it ( i bid on it) i believe it might have had something to do with space but i really dont remember. It looked interesting but was probably cancelled due to the death of the saturn. I think Nights is a good candidate but SOA, Sonic 1, Samba de Amigo are all good possibilities really to many games to decide.