I might be a well-known Shenmue fan, but I do think it has aged quite well, at least visually. Games that have "cutting edge" graphics for their time usually don't hold up visually (like Suzuki's other big franchise, Virtua Fighter). But for Shenmue they also put a lot of work in making it look good as well as making it cutting edge. Gameplay wise there still hasn't been anything quite like it in terms of depth, it may not appeal to people now but it didn't appeal so much to people back then, either. If you liked it back then you'll probably like it now for the same reasons, which is holding up in my book. I suppose the one thing that doesn't hold up is the English voice acting/localization, but I hate to hold that against the original developers.
I feel like many Gameboy Advance classics hold up quite well, Golden Sun, Advance Wars, Pokemon Ruby/Sapphire, Ace Attorney (even the DS additions feel really restrained with the 3D). It seemed they were at the perfect point between 2D and 3D, where playing the DS games feel less visually solid and more janky. I appreciate them trying 2.5D, but it doesn't hold up today when we see what the 3DS can do. I liked Pokemon AS, but in many ways it didn't feel like it needed a graphical upgrade, only the underwater segments add a lot to the game visually.
For me, I can't really name any N64 game that holds up visually... you really have to play them a while to look beyond the old spear-sharp polygons and pointed cone-boobs. The faces were done really well in OOT/MM, and they did what they could with what they had, but I would probably appreciate a total graphical revamp of those games more than any other Zelda game. Not only that, but the stylization the Gerudo and some Hylians always felt so ugly, when I don't think that was the intent. Out of all the N64 games, Super Smash Bros. probably holds up the best, and that's mostly because you're not getting a super close look at the models.
Most classics from the SNES era hold pretty well, for the same reason the GBA games tend to.