I don’t know if I really want it modernized, but I WOULD like to see Secret of Mana ported to a modern console. It was an old Squaresoft game for the SNES. Lots of fun.
Mine have been mentioned:
TIE Fighter
Master of Magic
X-Com
Very doubtful a proper remake is possible for the first two. A LOT of X-Com clone projects are out there, so maybe something will work out.
Funny to think that I’ve been playing these games off and on for 15 years! I’ve been playing Angband even longer, but that game holds up better and is still actively supported.
I want a Yoshi’s Island for the 3DS – When I they come out with a redesign I’m willing to buy.
Yoshi’s Island 2 for the DS was crap.
Did you try the Civ4 “Fall From Heaven 2” mod?
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The entire Ultima series.
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Have you tried the Dungeon Siege “Ultima V: Lazarus” mod? Somewhat dated by now, but still a pretty serious update. There’s an “Ultima VI project” one too.
What amazes ME is that anyone could play with the garbage that passed for 3D graphics on the original Playstation. I hated them at the time and bitterly mourned 2D, and to an extent I still do. I read an article a while ago that spoke what seemed like wisdom to me, in that old 3D graphics always look like ass, but old 2D graphics age better.
Hah! Yes I did! That was a lot of fun, if none too challenging or balanced. Might update well.
RE: Star Control 2: The voices are indeed from the 3DO version. They’re pretty good, but they’re optional in the SourceForge version of the game, at least.
Does that ship with the Civ IV complete set that steam sells? I tried some Ice Age mod that seemed to promise some kind of magic/fantasy theme, but got kind of bored with it.
+1
Centurion: Defender of Rome
X-Com - Or hell, ANY turn based squad combat game.
Archon Ultra
Elemental: War of Magic was originally planned to be a sequel to Master of Magic, but Stardock decided to create a new game world, and ended up rushing out a pretty lousy game.
However, they’re working on a standalone expansion called Fallen Enchantress that’s essentially a reboot. They’re basically going to try and pretend that War of Magic never happened and move forward. It looks promising.
I don’t know if it is or is not, but it is, to my knowledge, free and available… here?
Some already mentioned:
Baldur’s Gate
Morrowind
Grim Fandango
I was going to tell you that FO and FO2 work perfectly on my win7 machine, with killap’s fallout restoration project and patches installed. Those were fantastic, kind of like the “unfinished business” series of mods for Baldur’s Gate 1-2, and made a great game even better. Then, I tried loading FO just now, and had it completely hard lock my machine to where I had to cold boot it. That was a first for me in win7. I remember playing both though in Win XP and having it go well, FWIW. They’re very much turn-based, a little idiosyncratic with the Action Point system for combat, but incredibly rich in their story-telling and immersion. I guess you could run in XP emulation mode for both games.
I like New Vegas—still haven’t played FO3 yet—but it’s still much more of a shooter than either of the earliest games. I took pride in being able to talk my way out of most fights, and you just can’t do that as readily in New Vegas, even with the cheesy dialogue choices telling you that your Speech or Barter rank is too low.
Much thanks for the Harpoon-ish update news, and for the Janes flight sim love. (I detested 688i). I loved Fighters Anthology and spent more time playing Harpoon than I can count. Dangerous Waters doesn’t really compare, and I found it much more tedious and difficult to learn, to boot. Realism is boring, I guess.
18 years later or whatever it’s been, TIE Fighter might STILL be the best game I have ever played. With its expansions, it’s hours upon hours of absolutely riveting gaming.
An updated TIE Fighter - keeping the old awesomeness and gameplay, but just bringing it up to today’s standards? If it was as good as the original I’d pay a hundred dollars for it.
Hell, I’d be happy to get a full version that would work on my computer now.
Pong.
Lots of bits–less lag, better weapon condition checking (so you have to decide if you’re loading Harpoons or SLAMs on your heavy bombers), bigger scenarios (the original Harpoon couldn’t REALLY handle a Red Storm Rising-level conflict), longer scenarios with more objectives than kill 'em all (again, a convoy escort scenario that involved helping Europe hold out against the Sovs would be awesome, that tracked your effect on the ground war), modern units.
Twice I’ve loaded FO onto this machine. Not only does it lock the machine up, the machine crashes and needs a complete wipe and restore.
I love FO, but I’m not going to try to load it onto this machine again, unless I’ve backed everything up and I’m willing to take it in to the repair shop again.
I admit I’ve never played the original - I cut my teeth on Harpoon '97 which was pretty speedy, or so it seemed to me - since I was 14 and completely useless at the game, I didn’t play it too long 
That being said, you’re right in that even back then I remember thinking that it was a darn shame there was zero ground war (except fixed bases / SAM sites and such, and I don’t think those bases could change hands either).
That being said, a quick trip to the Wiki informs me that not only did the series not end in 1997, there’s one from 2007 (which apparently does include mobile land units !). Might be worth checking out. And hey, look, it’s still an ugly map with lots of itty bitty NATO symbols on it ! 
Sell your Cobra Mk. III and buy something cheaper that has a docking computer.
Alternately, you can add a mod to let you land on planets instead.
On my Amstrad CPC464 years ago, I far preferred the keyboard controls to the horribly clunky joystick, once I’d got the hang of it.
A game I have seen modernised is Lords of Midnight, with 3D landscape (as in, if you’re in the mountains your viewpoint is elevated), much better-rendered terrain, armies that look like armies (and ghostly images of other friendly armies that have crossed your path that day, reflecting the fact that movement should be simultaneous), and more.