Many games grow with time. Some become outdated and bested and do not. But perhaps it's not that simple. Super Mario Bros is certainly outdated and bested by its many successors, yet in hindsight it seems even more impressive for its time. This list is more on-the-fly than well-thought-out, although I've taken the above into consideration while making the (chronological) list.
Super Mario KartI haven't played any other racing game which I've enjoyed as much as Super Mario Kart, and that includes Mario Kart 64. So I guess it has to be on this list.
Teenage Mutant Ninja Turtles IV: Turtles in Time/Super Double Dragon
My two favorite sidescrolling beat em ups have yet to be beaten!
Super Probotector: Alien Rebels/Contra
Yep, still my favorite run n guns.
I thought that after having a bunch of Soul Caliburs around, this game would become moot. Well, I still love it. It has a slower pace compared to the newer titles, and I enjoy it much as I enjoy Street Fighter 2 after many years.
Micro Machines V3
We need more (racing)games with the main mechanic of Micro Machines! The running game Speedrunners utilizes it, and so should others.
Super Mario 64
They got so much right on the first try at 3D platforming it's crazy. The manveuering and camera controls aren't the best by todays standards, but the platform design is still super fresh.
Was not disappointed when replayed a couple of years ago. Still my favorite RPG.
Although it's very buggy and I don't wish to play it again, the open world structure of the game is still very impressive. I don't like open world for the sake of open world, but this game has reactivity and makes the open world feel like one world, manages to fill it with narrative and soul.
This is probably just me, but I still love this game and don't bother with any other area shooters, basically.
The Legend of Zelda: Majoras Mask
Could not appreciate the adult themes of Majoras Mask first-time around. It seems to have gotten a bit of a revival in the critical community the last couple of years due to its artistic integrity.
Metal Gear Solid 2
What made me appreciate Metal Gear Solid 2 on a whole new level and really see the MGS franchise in a different light was this article. Since then, the game has for me become the pinnacle of subversive play.
Silent Hill 2
Silent Hill hasn't delivered very much in the last 14 years, and I've gotten tired of most horror anyway. So this game, couched in psychonalytical themes, is still the gold standard.
Parsec47/rRootage/Noiz2sa (Kenta Cho)
After a couple of years playing a lot of shmups, I started getting tired of the lack of procedurality in most games. These three have a lot of it, and thus it never completely feels like starting over and just waiting to getting back to the level you were on before to give it another shot. Sadly, I've been searching for this type of game ever since and come up with, well, Geometry Wars, and nothing else I enjoyed.
Tony Hawk's Pro Skater 3
The formula was completed with this one, I believe. After that it was just a bonus, and not always a good one either.
The Legend of Zelda: Wind Waker
It was the first Zelda game for a new console that I played "as a grown-up". It couldn't have been anything else than disappointing, since the Zelda franchise (basically just A Link to The Past and Ocarina of Time) was such a big part of me growing up. I haven't replayed it since its release, but I have come to view it in a different light due to all the critical writing on it. And in retrospect it has perhaps even more weight, considering that the games that take place chronologically after Wind Waker don't have Ganondorf in them. So in a sense it's a goodbye to that villain.