In no particular order.
Xenogears (Squaresoft, 1998)
Xenogears is an RPG loved and hated in about equal measure. On one hand, it might just be the most impressively cinematic PS1 game ever made - the camera work, environments, dialog and writing are impressive and lavishly-produced, like a high-concept anime series on a game disc. On the other hand, its dragging pace, repetitious combat, mediocre dungeon design and uneven tone, as well as the fact that it was released very unfinished, earns it a lot of ire too. It was a game that was just a bit too ambitious for its time (and had a few too many cooks in the kitchen), and while Tetsuya Takahashi has tried again to replicate its success with games like Xenosaga and the Xenoblade Chronicles franchises, neither has achieved quite the same level of acclaim as the first one he made under Square. It'd be a lot of paperwork to sort out all the legalities and reassemble the original dev team, and convincing Nintendo to give a budget worthy of its scope would be a nightmare in itself, but I would love to see a remake that tells the tale of Xenogears as it was originally envisioned.
Fighting Vipers (Sega AM2, 1996/2001)
Phantasy Star III: Generations of Doom (Sega, 1991)
Mega Man Legends (Capcom, 1998)
Ultima 8: Pagan/Ultima 9: Ascension (Origin Systems, 1994/2000)
And a couple of honorable mentions.
Advance Wars - One of the games that defined the Game Boy Advance in its first year, it's an immensely fun turn-based strategy franchise that just abruptly fell off the map around the time Fire Emblem started to become popular. Probably no coincidence, but come on Intelligent Systems, there's still plenty of love for the franchise; bring it back!
Startropics - I know, I know. It's been twenty-five years since the last entry, Nintendo has no interest whatsoever in bringing it back outside of the odd Virtual Console or cloud gaming release, but I can always hope Mike Jones will emerge from the dust and go on another weird adventure with Zelda-inspired gameplay in a relatively modern setting, right?