Plenty of the old Star Trek games, like Klingon Academy, Invasion, and the old Microprose/Spectrum Holobyte games. If the modern professionally made stuff is utter trash, there's really nothing to lose by rereleasing updated games.
An HD remake of SD Gundam Generation F with updated rosters and 3D graphics would be great.
Another vote for turrican right here. One of my favourite amiga games.
Also psi-ops, but midway got into legal trouble, so a sequel isn't likely going to happen and nor is a remake in my opinion. If I remember rightly they were cleared, though. It's a shame as I've never played another game quite like it, the powers were amazing.
OMG THAT MISSION! Fuck me that was hard, but after mining that access road and holding off several groups of enemies, I left all of my barbarians guarding that choke point and retreated. They fucking managed to hold that point for ~3-4 incredible minutes. It was insane.
One of the best gaming moments in my life, and it was done on my very first PC with a very first game I ever bought for it [the next one was HL1 ].
Legend of Dragoon. I can't think of any game that would stand to benefit more from the improvement in graphics performance since its release given how strong the art and world design are and how clearly hindered both were by the PS1.
If not that, then I think the first Rayman game would be pretty awesome with HD assets.
And ideally, it's the final chapter in the entire saga, and it goes down like this: Kojima keeps making Big Boss games; however many he wants. One more after MGS 5 maybe? Or whatever. But it all builds up to a final game simply called Metal Gear. The story retells the events of MG1 and MG2. Grizzled, dangerous old Big Boss vs young, Solid Snake in his prime.
BB is commander of Foxhound and sends a rookie codenamed Solid Snake to sneak into Outer Heaven and rescue the MIA Grey Fox. Halfway through the game, Solid discovers the truth, that Outer Heaven is actually led by BB and fights him to a stalemate, BB escapes to Zanzibar Land, and in the second half, Solid is sent to pursue him. His radio contact becomes the newly promoted leader of Foxhound, Roy Campbell. Kaz is in it too.
Big Boss is voiced by Keifer Sutherland. Solid Snake is voiced by David Hayter. Some of the game is played as BB and some as SS.
It culminates with the iconic hand to hand fight between Grey Fox and Solid in the minefield, and is done in some Kojima way that becomes one of the most memorable moments in video game history, like the flowers in MGS3. And so does the fight that comes afterwards, BB vs SS. In the end, Grey Fox is presumed dead, Big Boss is burned up, and Solid Snake disappears. In the final shot, we hear Campbell reporting that he's gone and can't be located, but the visuals show us where he is. In the Alaskan wilderness, he's in a tiny cabin, drinking whiskey as he and all his sled dogs pass out near a space heater as a snowstorm rages outside. The Best is Yet to Come swells in the background.
I definitely think they should do it. Mainstream MGS fans have seen the beginning of Big Boss and the end of Solid Snake, but they haven't seen the reverse. They need to see the story that tells the end of Big Boss and the beginning of Solid Snake.