Bunch of great suggestions already so I'll add these:

Sid Meier's pirates!

Majesty

Gothic (it's actually getting remake, but if the intro they've showed is anything to go by, it's gonna be a disappointment. We'll see..)

Far Cry. Both FC3 and FC4 were great, and then they never made another one after that.

Legend of Zelda following Twilight Princess.

TimeSplitters following future perfect.

XIII following... the ending of XIII cliffhanger.

Half Life following HL2 E2 cliffhanger... or L4D3... or Portal 3...

Overwatch following Jeff Kaplan

Cave Story following Cave Story 1

A new Final Fantasy Tactics and I mean one like the classic PS1/PSP game not those strange Advanced titles.

Bomberman! 💣💣💣

Jazz Jackrabbit. Poor fella's been abandoned for over 2 decades now. Really fun platformer, a 3rd game was in early works, but Epic ditched it to focus entirely on Unreal

Star Wars Jedi Knight series. As is, there's Dark Forces (Star Wars Doom), Jedi Knight (Star Wars Quake 2), Jedi Outcast (awesome) and Jedi Academy (good, but JO is overall more polished). Thank fuck the years of EA-exclusive Star Wars games is over. There are several other SW game series that deserve to make a return (Republic Commando, X-Wing/Tie-Fighter, KotOR), but my first vote would go for Jedi Knight

A bit of an obscurer one, but I would love another Black & White, based on Black & White 2. It's a god game where you control a giant bipedal creature, control a city (or several) and battle against other gods through architecture and combat. You can train your creature to do things you prefer and expand your influence however you like.

It had a good/evil morality system, is completely winnable by being a pacifist, and has a really cute style of humor.

No other God game has quite scratched that itch and it's still fun to this day almost 20 years later.

Would love to see a Dark Cloud 3. Not PlayStation exclusive though.

Transport Tycoon Deluxe

Of course there is always OpenTTD, which has by far exceeded the original, but I would just like to see a modern game (not necessarily in terms of graphics) with the same vibe. Transport Fever and all the other variants never quite achieved the same depth and complexity.

Nostalgia drive engaged !

The Crusader series (No Remorse, No Regret) could have been built upon, with its famously cheesy live-action cutscenes.

The Quarantine series disappeared after its second installment, Road Warrior. Come to think of it, most mainstream vehicular combat games went away, like the Interstate series.

The Discworld adventure games (1, 2, Noir) were famously convoluted, but they did a pretty good job of adapting Pratchett's world into video games.

Finally I would have liked to play the initially planned sequels to Advent Rising. I have (probably rose-tinted) fond memories of that game, but hey, you asked.

NFL 2K. NFL 2K5 was so good and scared EA so much, it led to the EA/NFL exclusivity deal and the death of the entire football game genre for the last few decades now.

A lot of people will disagree, but I loved Star Fox Adventures. It was easily my favorite Star Fox game.

3D Rayman games, the only one I played was Rayman 2, so that's all I can go off of.

BIONICLE, the game to the movie was a bit janky, but so much fun!

Pokémon Rumble: I remember only liking the first one (didn't play the second), and really disliking Rumble U. There's a mobile game now apparently, but...no thanks.

A very obscure one: Onslaught, from the Wii Shop. A first person sci-fi shooter with Wii motion controls, playing on an alien planet with giant bug creatures. Quite reminiscent of Helldivers or Starship Troopers.

Asura's Wrath: I think a remake would be nice, not sure if there's much space for a sequel, the ending fit quite nicely.

Xenoblade Chronicles X: I'm gonna count this as its own franchise separate from the other Xenoblade games, and a remaster, remake or sequel would be amazing.

Bonus: Borderlands 2 had a good setup for a sequel, an incredible villain and such great characters. I'd love to see where they'd take their stories, like Maya & Krieg. Should be about time for Borderlands 3, I'm sure it'd be great! (FUCK WHYYYYY)

A good comment& conquer game

Jak & Daxter, definitely. I want to know more about the whole Mar lore

Ultima

You know what, fucking Bubsy. Let's see another one of those fuckers. Let's give it to a dev like insomniac though. That's what I want to see. Let's take something that never quite pulled it together and make that shit shine! Give Bubsy his chance in the sun.

There's a fair amount of failed mascots that had small followings or good ideas badly executed. Instead of rehashing the already beloved, let's see some genuine attempts to redeem some of the benchwarmers.

I want to see Ultima Online come back, also Legacy of Kain

Intelligent Qube

Not a series, but I'd like another.

I’d love to see a modern take on Cannon Fodder, as well as another entry in the Desert/Urban/Soviet/Nuclear Strike series.

Lastly, there was a very fun demo/mod to Sensible Soccer for the Amiga that set the match between UK and Germany, and replaced the ball with a bomb that would periodically explode and eliminate any nearby players. I’d live to see a modern-day version of this, honestly - just some goofy fun!

..and yes, I am fully aware of just how old this makes me all sound.

Here's a rather wacky one: Star Tropics. A sequel to Zoda's Revenge would just blow my mind.

Spectrobes, spent a ton of time in all 3 games as a kid. Apparently the 3rd game sold pretty poorly even though I would argue it was probably the best of the 3. It had just about everything one would want from a pokemon rpg, it even allowed for 2 players! Super upset that Disney killed it :(

New entry should absolutely follow the footsteps of the 3rd game (origins). Only thing I would hope that is improved is some of the terrain paths were kinda narrow and hard to accurately maneuver the horse-like mount around. That super frustrated me as a kid as it was much faster than walking, but all the time you ended up losing from getting caught on terrain, having to dismount/dismiss the mount, turn around, then resummon/remount made it more efficient to just walk.

The combat was fun enough on the 3rd, but my absolute favorite part was the excavation of fossils. Trying to go as fast as I could while also being super careful to not damage the fossil and having that linked to better stats for spectrobes was SO much better than breeding/catching new pokemon to me. It felt much more engaging than hoping for good rng.

If they won't make a new one, the least they should do is remaster the games for switch. Which they also probably wouldn't have to do much for the remaster as I would argue even the original version looks the same/better graphically than the latest pokemon releases for switch.

I would love a sequel to quake 3 arena as another arena blast em up game, and one for gta2 as another top view game

Ape Escape. I would love one with the scope of areas similar to Super Mario Odyssey

THPS 3+4 please

Parasite Eve, hell even a remake of the first would be welcome