I would suggest the the Playstation (1) and Sega Saturn era of the late 90s was the best time for me.
Many people will remember how advanced Sega Rally, and to a lesser extent Daytona were for their time, with a level of realism not seen previously. By the end of this era we would also see Gran Turismo and Gran Turismo 2 raise the bar of acceptance for the standard of racing games.
It would also change the way many people viewed gaming with the introduction of Lara Croft in the first Tomb Raider games.
In a previous podcast you hinted that you weren't really aware of Tekken, but you will definitely remember Virtua Fighters, which was the Sega alternative.
Of course everyone is welcome to their views, but the PS2 and Xbrick, as well as the current PS3 / 360 have not really introduced very much apart from online play and the multitude of generic first person shooters that have been released. With so many of these being more or less the same (same wars, same 11 year old kids screaming down the mics, and same campers sitting with their sniper rifles getting 1 headshot per hour) I have really lost any interest in this genre.