Looking back to my first console, the Atari 2600, I had a good time with Pitfall 2. Skip ahead a bit to the SNES and it was Starfox courtesy of the FX chip. N64 had Perfect Dark, which book ended rather nicely with the console launch window title GoldenEye. Then on PSX, I enjoyed titles like Front Mission 3 and Vagrant Story. PS2 more or less concluded it's illustrious carrier for me with Shadow of the Colossus...rather fitting since it began with Ico.
Of course the reasons for most video game systems finishing strong comes from developers learning how to get every last drop of processing power out of the hardware. As an added bonus the price tends to be a bit cheaper than usual as well. I can remember picking up Vagrant Story for $30 at a local Best Buy electronics store because they were doing an inventory clearance sale to make room for next gen products.
Regardless, don't get overly nostalgic, or conversely too excited about the future. Right this moment is the best time to be into video games in a long time (and most likely for a long time to come).