UPDATE: Thanks to the community for pointing out many PS1 and PS2 games are available on the PSN store for PS3 and PS4 respectively. Maybe Sony's can someday make them playable on all of their consoles.
I like games. I hate missing out on good ones. So therefore I like how fewer exclusive games means I buy fewer consoles.
This list runs the risk of quickly becoming outdated. Just last week they announced Shin Megami Tensei III Nocturne would be re-released which is what I wanted ten years ago, back when I cared. I'm happy the game is getting a second life. But let's be real, there are too many games still gone without a re-release. Only a little while ago all Kingdom Hearts games became available on Windows, which I didn't even know I wanted. Besides the potential for mods, I need to remind myself the game can be bought and played on the same system I type this from. And then shortly afterwards I hear we will be getting a FF7: Crisis Core remake.... how about that. In that case, I hope this list becomes outdated if it means even half of these games get made re-available
A year ago I would have been asking for a Medievil remake and lo and behold they went ahead and did it. Before that it was Crash and Spyro and those came and dominated. I remember lamenting not picking up Little King Story for the Wii before Steam patched up that fault in the universe. I waited a long time for a Shenmue 1 & 2 HD release and then it did arrive and I have yet to play it. I had given up hope for a Banjo Kazooie or Blast Corps re-release before Rare replay. Destroy all Humans would have been on this list but... y'know.
I'm expecting a Timesplitters HD trilogy to drop any week now.
Without further delay,
The List :
Last story / Pandora's tower

I love both these games but not enough to dig out my Wii, maybe next holiday. A graphical touch up could be exactly what they need. Both games had enjoyable combat and it could be given new life on a new system.
Shadow hearts 1-3

This one might be a hefty task if it's all 3 games. As they are, they wouldn't attract much new attention and any upgrading of the textures would be a big job. A remake would be on the cards but it wasn't broke the first time around. I've been very pleased to see the games are remembered to this day. So maybe, someday, we can have nice things, these will happen and the world can be a little more whole.
Rodea Sky Soldier

This one is just for me to enjoy. I don't think it got a fair chance. Sometimes what the Wii offered, needs to be taken away. Some games are more than their gimmicks.
Silent Hill

Not a big complaint because I still own the working originals but they could use some TLC. Has to be better than the physical HD collection.
Brave Fencer Musashi

Did not get to play it, but I would like to.
Xenosaga / Xenogears

So I can get a chance to play them and I think it would sell well despite what the creators say. Hell, the spiritual successor series has gotten HD and handheld ports of it's most recent games. This one is baffling.
UPDATE: Xenogears is indeed available on PSN for PS3 but not in EU.
Panzer Dragoon Saga

I think this game needs no introduction, the internet has done all that for me. So where the hell is it? I have the money for it, charge whatever you want. Even just port it, forget the visual updates. Let. Me Play. THE GAME!
Ring of Red

I liked this one. Think with some quality of life updates and it would be a real winner.
Silhouette Mirage

Didn't play it. Found it's Wiki page by accident. Now I want it.
Tales of destiny I & II

Just release the damn games! There was no issue with the others in this series.
Suikoden series

There are a few entries in this series I had simply given up on ever playing because of how rare they were.
The Legend of Dragoon

I want this because I didn't get a chance to play this and it's a damn shame. It seems lost in license limbo and that makes me sad.
Donkey Kong 64

I'm not alone on this one. Add in-level character switching and it's done and ready.
Space Station Silicon Valley

This one would be hard to play today so I get that it would take some work. I suppose I don't mind too much since I still have my original copy.
Mystical Ninja Starring Goemon

I only recently discovered the SNES game so this should be the next one up for purchase... sadly that can't be the case right now. All reports tell me a direct port would be enough, since as it was, was good enough.
Ape escape

MGS3 got me curious, a banged up PS1 copy got me hooked. The ball is in their court now.
Vagrant story

Seriously, where the hell is it?
UPDATE: Vagrant story is indeed available on PSN for PS3 but not in EU.
Tomba 1 & 2

I would do alot and pay alot to have this game made easily accessible.
Eternal darkness

Maybe if I just forget about it, it'll happen all on it's own.
Lost Kingdoms

I've heard reports and read reviews that had both positive and negative things to say. I would like to decide for myself but I can't.
Blinx 1 & 2

A few tweaks to rebalance it and you've a solid game to give.
The Sims 2

Won't happen because EA.
The Warriors

I want because I have not played. Let me correct this... please.
MGS4

I mean, come on! I sometimes shiver at the thought my PS3 will die, with no replacement models and the game becomes an inactive ornament. Don't give me any of that backwards compatible crap!
Baten Kaitos & its sequel

You ever look up the price this game goes for? I accepted a physical copy was a lost cause long ago.
Little Samson

Seriously? No Nintendo VC store release?
*shakes head*
Mother 3

Do I even need to elaborate?
Zelda Oracle of ages / seasons

How dare you force me to turn toward emulation! The GBC card died long ago from exhaustion.
Viewtiful joe

Cause it's awesome
Dark Cloud 1 & 2

Level 5 have proved their worth, let them have this.
UPDATE: These games are available for digital download on PS4. Dammit Sony!
MGS : The Twin Snakes

Deserves another shot. Regardless of all the games faults and a fine example of why not to do a HD remake, it should still be made widely available.
Mario Kart: Double Dash

Did no one else enjoy two players in the one car? Almost all the tracks got carried over to the next few games so it felt like this one got left behind.
Star Ocean 1-3

These games are always almost good. There's always too little space exploration or too many cutscenes, or too lazy voice acting or too much of the non-space age planet. I don't want a remake I just want the games with some quality of life addons. There's even some days I miss the combat. I know plenty of people who want to give the third game another spin and it being on PC would be an immediate purchase for them. Star Ocean 2 got a lot of love in its home country and I am very jealous.
UPDATE: These games are available for digital download on PS4.... I guess Steam wasn't
bankable good enough.
F-Zero GX

I brought this game to a party a few years back and we played it on my friends Wii and it sent a shock of electricity into that room. The same friends still ask about this game. This game is more famous for being difficult or for ending the franchise than being a good time, which it is.
Star Wars: Rogue Squadron II

I blame no multiplayer for this one. It was outright idiotic to make this a Gamecube exlcusive. The only worse decision was to keep it that way.
Jet Set Radio Future for Xbox

I know I'm not alone on this one. Licensing issues might mean it is easier to make a spiritual successor.
Hotel Dusk & The Last Window on DS

Just a shame really. Thought the jump to PC would be easy. Ghost Trick got an ios port.
Jeanne D'Arc on PSP

It was a hard game to come by. It got an awful lot of praise so I'm just curious.
Boom Box on Wii

This is like many games which were intended to be ported but accidentally became an exclusive, which is where it has stayed. I guess Spielberg wasn't too proud.
Muramasa: The Demon Blade

This one got a PS vita re-release. I'm not sure that counts. From the same developers who made Odin Sphere on PS2 which could also be considered.
Valkyrie Profile 1 & 2

I own these games but I want others to aswell! I'd gladly buy them again.
Vandal Hearts 1 & 2

....why not?
Threads of Fate

It looks fun. I'd like to try. There have been worse reasons for a re-release.
Arc the Lad trilogy

I'm sure it has it's fans. I would like to become one.
Alundra

People still make Zelda clones, why not just dig up some of the old good ones? The world is weird, man. I can take or leave the sequel.
Lunar: Silver Star Story

This game got a full upgrade for PSP and then that was that. No further movement. PSP games were slim pickings where I'm from. I want all of them but I know not to ask too much.
Lost Odyssey / Blue Dragon

I see these two get brought up often enough that I also wonder about them, even if I was never a fan of either game.
Fable 2

The other two games got a port. I've been loud about this one in the past, so no point stopping now.
Black and White 1 & 2

Some would probably just take the second game. Let us remember Lionhead studios fondly.
Daxter

Alotta fun. ...There was a time when that was enough.
Uncharted: Golden Abyss

I'm sure they have their reasons, they choose to keep them private so I assume those reasons are bad and expensive.
The Neverhood

I don't mind so much since I own a copy, and I doubt those who made it care much about the property after it bombed. Would be nice to see on GOG or something.
Red Dead Redemption

I'm convinced Rockstar wants to keep all those, what can only be amazing, mods for themselves.
UPDATE: By demand of the beloved commmunity, whose undying love of games is only matched by their desire that they be made as digital releases.
Skies of Arcadia
I never played this game. Couldn;t get ahold of it. Gee, wonder why that is? I never had a dreamcast and to own a physical copy of the Gamecube game was close to impossible in my little corner of the world.
Honorable Mentions:
Soul Reaver - This game is rough nowadays. Honestly, it would call for a full remake, and do the second game while you're at it. I experience disbelief that these games don't get seen with all the potential cash to be made on their uniqueness alone. I guess that's why it's not up to me. The Steam ports are pretty lackluster but you take what you can get I suppose.
Spinter Cell Trilogy - These games were given a HD collection and... lets just say it was a bumpy (and stretched) ride.
Sudeki on Xbox - Looked fun, a friend lent me it but it wasn't backwards compatible with the 360. Was sad.
Sin & Punishment for the Wii- The Original is on the VC. This game came out on Wii and is now on 'Nintendo eShop' so it's about halfway there.
I've probably barely scratched the surface with this list. There are innumberable PSP and Gameboy games that could have been included on here. Let me know which game you can't get modern digital access to thanks to whoever owns the rights. I would love to hear about all of them.
LOOK WHO CAME: