1990s:
Car and Driver (PC) https://www.mobygames.com/game/dos/car-and-driver/screenshots
Microprose Formula One Grand Prix (aka World Circuit in NA, PC) https://www.mobygames.com/game/world-circuit/screenshots
POD (PC) https://www.mobygames.com/game/windows/pod/screenshots
Screamer (aka Bleifuss in Germany, PC) https://www.mobygames.com/game/dos/screamer/screenshots

2000s:
Wave Race Blue Storm (Gamecube)
Burnout (Gamecube and Xbox)
Project Gotham Racing 2 (Xbox)

2010s/20s:
Forza Horizon 3-5
several Mario Karts (8DX is my fav)

I've played GT Sport far more than any other racing game, so it's the obvious choice for now
https://www.gran-turismo.com/us/gtsport/user/profile/1495257/history/driverStats

GT7 has the potential to overtake that, but it has a long way to go before even getting as good as GT Sport was. The online mode is a big step backwards so far. However custom endurance races are sublime, most fun racing I've ever done. This is a compilation of my 12H run last weekend.

Full day/night cycle, dynamic weather, heavy damage, no 2 laps are the same.

My first racing addiction was Hyper Rally on the MSX, then Indianapolis 500 on PC and Lotus Turbo Challenge on Amiga 500.

Grand Prix Circuit, Test Drive, NFS, Wipeout, V-Rally, Burnout, Colin Mc Ray Rally, Rallisport Challenge, Project Gotham, Midnight Club, DriveClub, Motorstorm, Forza Horizon, Dirt Rally, all favorite series. And I played so many more. I never got into Mario Kart though, must be the power ups since I avoid them in Wipeout as well. I only like the races without weapons.

My two favorites are FlatOut (2006) and Dirt2 (2009).

Just tried to look through the games I have added here in the past and it seems you can't order them by genre, although the Game Stats does give me my favourite genre :/

First racing game I played was F-1 Race on the GameBoy. Was impressed with the pseudo 3D graphics you could pull off in 2D. Racing didn't really feel right to me until it went 3D, although I did enjoy some top-down 2D racing games such as MicroMachines or GTA2.

Nevertheless, after GameBoy and MegaDrive went into PC gaming back then NFS games such as Hot Pursuit or Most Wanted filled this genre niche for me but I hated getting stuck on the scenry. Later on I loved the OG TrackMania.

As you might notice my preference is with arcade racers and when I returned to console gaming Mario Kart took that spot. MK8 tracks has such course design, elevation and slopes that it didn't feel flat at all, such a blast.

In the past I didn't consider myself a fan of the racing genre, but progressions have gotten me more involved in this genre over the years. I only played games like Mario Kart and I would rarely have another IP of racing genre. I've always liked the idea of unrealistically fun, non-conventional racing games. I did play Starwars Pod Racer for the N64 and Z-Zero GX for GC, they have a place in my heart. I also had Kirby Air Ride (Loved the city trial mode in the game), I was obsessed for years with this game, I would play the city trial mode over and over again..

I've always liked the graphics in realistic racing games/simulations and found them fun to play in the moment if they were already loaded up in a game shop or when round a friend's house but I would never go out of my own way to have a copy any as I was never too exited to play realistic racing games until VR happened.

Wipeout Omega Collection on PSVR is amazing and really fun. I would put it in my top 5 overall VR games of all time. It is realistic enough to separate it from other racing games I mentioned above and the VR makes it even more realistic, yet it is still an unconventional futuristic game and not a conventional driving simulation/game. Playing VR has made me want to some more realistic PS5 racing games/simulations for the PSVR 2 when that comes out :D.

I bet proper realistic racing games such as Forza Motorsport, Gran Turismo, Need for Speed, etc would look and feel amazing in VR, especially if you imagine what they could do if they pushed the 9th gen level of graphics. That would be super immersive.

A rundown of run racing games I have liked over the years:
Mario Kart (particularly the newer MK games especially MK8)
Kirby Air Ride: (City Trial mode)
F-Zero GX
Starwars Pod Racer (N64)
Wipeout Omega Collection (PSVR)

I really don't like racing sims, which pretty much only leaves Mario Kart and it's copies these days.

Some of my favorite racing games which are not Kart racers:

4D Sports Driving ( aka Stunts)

The game is quite buggy, especially on tracks with many jumps with a Porsche mach Indy. But these bugs don't crash the game (except in the notoriously unstable track editor), they just cause hilarious car crashes with them flying hundreds of meters into the air and the like. Like this one for instance:

Extreme G-2

I love me some Vehicular Combat. Sadly, such games have become very rare, and good ones even rarer. This was one of the best ones. And yes, unlike most, I played the PC version, not the blurry N64 version.

Carmageddon

Mayhem doesn't even begin to describe this game. You don't even need to race, just eliminate all the competitors and you're the winner. Squashing everything in sight is just a bonus.

Flatout & Flatout 2

Like the previous game, you can destroy everything in sight. Unlike it, you have to actually race. And you can choose and upgrade your car. And the minigames based on ragdoll physics are just hilarious.

Fatal Racing/Whiplash

Still my favorite racing game, especially in Multiplayer. Hard to explain , so better watch to video. 

There was also Extreme-G III and Extreme G Racing Association for the PS2 generation of consoles.

After having played the excellent Wreckfest, it is really hard to go back to Gran Turismo. Wreckfest has superior AI, physics and damage model. Gran Turismo feels very dated in comparison. I know the games aim for totally different things but that is how it feels to me during actual gameplay.

I wish Motorstorm would return to Playstation. Pacific Rift was such a cool game.

Currently I'm only into Mario Kart but I used to be also into Need for Speed and Gran Turismo, sadly NFS went to the sh*t after Carbon (so like 16 years ago) and stopped playing them, and GT games after GT6 have problems that make me feel not compelled to ever get them, such as GT Sport not having SP content or GT7's SP mode being online only.

Edit: I also used to play Formula 1 games.

Same for me in terms of Need for Speed.

And one series I forgot to mention which I played a lot a dozen years ago was Burnout, especially Takedown and Revenge.