In terms of newer games, I think the Middle-Earth: Shadow of Mordor/War are worth playing. The nemesis system offers a mechanic that you can't get anywhere else.
Ecco was one of those games that I did not get as a kid, much like Tetris. It wasn't till later in life did I start enjoying it. But Panic on Funkotron was always a favorite.
I felt bad about Starflight vs NBA Jam. They're both great games for completely different reasons. It just depends whether or not you have someone to play with.
I was born in 1985 and I've done everything on this list with the exception of Columbia House because even as a kid I could tell it was a scam. I imagine even people born in 88-89, deep into millennial territory, could say the same.