Well, let's get the unlikely ones out of the way first...
Silent Hill 1 Remake - Fans have been clamoring for a remake of the first Silent Hill for a good ten years now. The original is still amazing and holds up today in terms of atmosphere, music, story and (surprisingly) gameplay. The one thing that has always held it back is its graphics. Compared to SH2 which features beautiful graphics and visuals that still look pretty good today, SH1 looks extremely dated. The thought of experiencing this game's incredible story with modern graphics, seeing characters like Harry Mason and Alessa in ray tracing enivironments.... is just breathtaking.
At first I was against a remake because I think it would create big problems with the lore which is perfectly synced between SH1-SH4. Then I realized that we already have lore-breaking games such as Origins and Homecoming that **** up the universe completely, plus you could always do like developers always do and proclaim that the remake is not a remake but a "reimagining" that takes place in an alternate timeline. Unfortunately a remake will never never never happen because Konami owns the IP, and they don't know **** about how to treat their properties. Especially Silent Hill.
SSX Tricky Remake - If there's any game that would be extremely fun to experience with modern graphics, it's definitely SSX Tricky from 2001. The game just screams the early 00's and features so many colorful and unique characters. The tracks are insane and over the top, and I think a remake should make them even bigger and have more shortcuts. If possible, I'd also love to see new tracks added to the already exisiting ones. Unfortunately, the IP is owned by EA so a remake will never never never happen. However, Steve Rechtschaffner who was the producer for the game said last year that he's currently working on a spiritual successor to SSX called "Project Gravity". Although I'd rather see an actual new SSX game with him behind the wheels, that might be the closest thing we'll ever get to a remake. As cool as it is to know that Rechtschaffner is working on a new snowboarding game, it's going to be free-to-play which is never a good sign these days. It will also be a low budget game, that's for sure.
Other than those very specific two, I'd also like to see remakes of the following games (that are more likely to happen, too):
Red Dead Redemption 1
The thing about Silent Hill 2 is that they were asked, because they knew the game system could load faster, would they keep the fog. The fog, apparently, initially was put into Silent Hill 1, because the load screens couldn't load faster enough when Harry Mason was running down the street (correct me if I'm wrong). Those foggy streets, a lot like Resident Evil door and stair load screens, became an icon of their respective games.
Btw, I really feel they should at least provide DLCs for REMAKE3
They need to include the clock tower, because they never really did. They need to fill in the gaps. They rush through the game. They skip a lot of parts. And other parts were simply left out.
The game's way too short, you can literally finish it in one and a half hours. The game plays more like a really long demo.
Don't get me wrong, I actually enjoyed playing it, I just wish they had finished it.
As far as Dino Crisis goes, if they ever do remake it, I hope they provide more bullets, rather than those ridiculous tranquilizer darts. Two minutes later, the raptor is awake again. And I still haven't finished searching the area. And no repeating enemies this time. Once they're down, they're down. If I shot a family of bears, do you really think they'd keep on showing up over and over again, as I walk through the woods? Nature doesn't work like that. I don't care what era you're in.
I would kill for a Parasite Eve remake, even if it fails to capture the essence of the original. As long as it's a serious attempt at a spiritual successor, stays faithful to the plot, NYPD theme, Aya, and Eve, and keeps the unique crafting system in some form or another, I will be happy. Surely there's some childhood fans of it working at Squeenix? (I do not keep track of the comings and goings of Squeenix but surely they still have some funds and talent left?).
Parasite Eve 2 I also love, it's so relaxing, has a good gear system, but asking for a remake of that as well may be a stretch.
I just realized that I forgot to mention one of the most badass 90's games ever, Urban Chaos released in 1999.
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Man, I played this game at my friend's house like crazy when I was 11. It was VERY ahead of its time and had an extremely impressive combat system, allowing you to kick and hit your enemies in so many different ways. It also featured open world, car and pedestrian population, leaves physics and even friggin' water reflections! And remember, this was before GTA3. Man, this game deserves so much more love and credit for what it has contributed to the industry. Sadly it's a lost gem that's only remembered by a small clique of gamers.
It would be absolutely incredible to have a modern remake of this one. I mean, it even has a pretty good story with twists that leaves you shocked.
Yes once you get a good grasp of how the game works, it's quite an intoxicating experience, once you get past the initial learning curve. A modern take on it would be welcoming but they would have to do it right! Not just slap a theme on there and call it good. Jill Valentine and Aya Brea would have been the ultimate female game character competition which unfortunately never transpired.
Which brings us to the problem of Japanese games today, aside from RE2R remake and Capcom, I feel that Japan is losing its verve in game design, and Western developers have largely overtaken them lately which is a vast turn around from the 90's, where Japan was king in games. Japanese culture is very backwards though and has a tough time evolving, so that might explain a few things. Everyone from the West who has moved to Japan says its like going back in time to the early 1990's, when Japan's economy really started slowing down, they simply have no desire to modernize or innovate these days and even South Korea is doing a better job there, yet there are no major South Korean game developers....
China has a very budding game industry going and the few Chinese games I've played show a lot of promise so if "democratic" Japan or South Korea cannot get their **** together then "authoritarian" China could very well fill that void in Asia. Since Japan and South Korea both HATE China, shouldn't that be a motivating factor to modernize? No?
Edit: Looks like there's whispers of a PE remake or at the very least, remaster (I would be equally thrilled with a Steam release remaster of the game because it least it could could definitely retain its integrity w/o risk of screwing everything up in a remake).
Two of my dream remakes have actually been confirmed recently which I thought would never happen, and that's both Max Payne and Max Payne 2: The Fall of Max Payne. Remedy got in contact with Rockstar and Rockstar has allowed them to remake them in their Northlight Engine, which is a dream come true considering Rockstar has just been holding the IP hostage.
And even though I've never played the original, I would love to see Dino Crisis get the Resident Evil 2 remake treatment only because more survival horror in the style of REmake 2 could only be a good thing and because dinosaurs in general just seem very underutilized in gaming.
Assassin's Creed has grown so much over the years too that I'd love to see them go back and remake the first game. Part 2 was such a leap from the first one and all the older games in the series have been remastered already except for part 1, which has aged so poorly with its primitive parkour and combat and repetitive mission structure.
Red Dead Redemption is also a no brainer. They've basically remade a huge portion of the map already for Red Dead Redemption II, they have tons of updated assets and mechanics. The story of Red Dead Redemption II does so much to enhance the original's narrative that it would be unfortunate for them to never revisit it and make the 2 feel much more cohesive.
A few of you have already listed some of the major titles I'd want to see remade.
Code Veronica is a given for me and I don't think I need to go into detail on why it deserves a remake but I am baffled at Capcom not capitalizing on such an opportunity. The chance to see Stephanie Panisello's Claire again and to also see Chris and Wesker's feud more fleshed out- what a shame if Capcom really chooses to look past this for the series.
Not sure if this is a real discussion with Rockstar but a remake of Red Dead Redemption seems almost warranted for reasons explained by @Turo602.
I'm going off on a tangent here but I'm disappointed that Rockstar hasn't bothered with doing any fun DLCs for RDR2 like they did with RDR Undead Nightmare. The DLC was pure gold that I was convinced they'd surely do it for RDR2 as well- if not with zombies then an alien invasion that Arthur and co have to fight off... but they didn’t.
While the first Silent Hill game is the most deserving of a remake, I'd love to see any of the first four Silent Hill games remade properly with stunning graphics and mechanics.
The Dino Crisis series, as mentioned by a few of you now, is another no brainer that's worthy of remakes. REmake2's gameplay style would indeed be very befitting for the series and the threat of dinosaurs would be a refreshing take for survival horror video games.
Predator Concrete Jungle. OK, they don't need to remake this exact game but I would absolutely love it if we could get a Predator game in the same vein. A story-mode where you play as a Predator again hunting people and other creatures in various settings. Just take my money.
In all seriousness, nothing really stood out to me for remakes so I started thinking about games that I absolutely loved and enjoyed when I was younger and 2 came to mind: Hybrid Heaven and Ogre Battle 64, both were released on the N64. Not really dying for these to be remade but it would be sweet.