I played FlatOut with keyboard and found it okay to control, but whether you've got 4wd or rwd or fwd really makes a huge difference in the controls. Part of the fun of the game though is the feeling you're not quite in control and still manage to pull through and wreck someone else.
What made me really like Trackmania back when I initially got that was actually mostly the feel of it like the old 4D Stunts game. First release even had 8-bit chiptune style music to go with the menus.
My personal favourites for racing games, not really available on Gog sadly: Crazy Taxi 3, okay not point to point racing but still a to b as fast as possible.
Mashed was a bit like Death rally but a bit updated compared to it.
Outrun 2006 is nice to just hop into for a few races, and when you're tired of stage races you go for a ride with your girlfriend and do silly tasks like avoid aliens or count cars.
XPand Rally, likely the most entertaining Rally game I've played. Okay obviously I prefer fun arcadey controls over simulation, DiRT was frustrating to me. XPand Rally used the same engine as the FPS Chrome did. Unlike the Colin McRae games you feel like you're plopped into a world, rather than on a track with some area to the sides. The alterations to your car can be very easily felt, and the engine does sound different depending on transmission settings, tuning kits and such.
And for violence. Carmageddon. Any of them but the 2000 one does actually feature a story. Not a particularly good one, but a story nontheless.

my favourites aren't on gog - Carmageddon and Motor Head.

If you want racing simulation, then go for the games of SimBin.
Like GT Legends, GTR, GTR 2.
The Test Drive serie is also good, like Test Drive III or the last one Test Drive Unlimited.
Or go for Trackmania Nations Forever.

I you just want some arcaderacer, then Need for Speed is good enough. But be sure to grab the first serie, like porsche challenge, hot pursuit, etc.

And if you want some crazy racing, like with destroy each other or something like that, you can look for something like Destruction Derby or Carmageddon.

I could cry. Thank you Wishbone - I've been looking for Death Rally for years, and the copies I've found just don't work. And it's actually:

1.) Rereleased to work on current rigs
2.) Free

Thus 1 + 2 = +1 rep. You rock, good sir. Time to finally try and beat that frigging Duke Nukem!

Grand Prix Legends. The fact that it came out in 1997, and still has an enthusiatic fanbase that produces patches and graphic upgrades to make it run smoothly on modern computers tells you something.
It was never a real popular game...it is a very realistic, very demanding game, and the original release did not have an arcade mode (this was fixed in a patch from Sierra) but if you want to know what iwas like to drive in the GRand Prix in 1967....the last year before new rules ended the "bad old days" of a high driver body count .....this is the one. It's like stepping into the world of the film "Grand Prix".
And, yeah, I would like this to show up on GOG.

Burnout Paradise.

Depends on your taste, I think.

I like Rally Racing, and there is just one good Rally Racer out there:
-Richard Burns Rally-
but be aware...before you`re allowed to drive a real race, you must complete the rally school.
And that can be very frustrating - believe me.
But after you ended school successfully, you are rewarded with a rally sim, which deserves that description in a way, no other rally racing sim does.

As for the racers here on GoG: I would go for Flatout - it`s a nice fun racer (no sim), and ...if you liked that...Flatout 2

Trackmania Nations is also a lot of fun. Very addictive.
Burnout Paradise is also nice.

Flatout

I can actually manage to win races, unlike in GRID where even on easy and with all the assists I come in dead last after wiping out a dozen times.

You're very welcome :-) Death Rally is fantastic. And Duke Nukem CAN be beaten ;-) The only thing about the game that I find slightly annoying, is that whenever you buy a new car, you need a couple of races to adjust to the more sensitive steering. I tend to hit walls a lot right after buying a new car.

Legitimate Simulations:
1. iRacing (really f-ing expensive tho)
2. rFactor
3. Richard Burns Rally
4. Live for Speed
5. Nascar Season 2003

Arcade Racers
1. Need for Speed: shift (sorry it just isn't realistic actually)
2. Trackmania Nations
3. GRID (NOT REALISTIC AT ALL)
4. Screamer 2
5. Xpand Rally

Racing Games I hate but ppl love:
1. DiRT (far inferior in every aspect except graphics to RBR)
2. Gran Turismo

Sorry but as someone who's had a taste in real life professional racing and played simulations a lot. Those top five sim games I've listed will probably never change because most people actually dont understand how hard racing can be. Seriously, play any one of those 5 games and compare them to everything else and you'll see why only those 5 games can be considered a true sim

Well, i have to go with the 3 best arcade racers ever made (in order of importance):

Carmageddon 2
Flatout
Flatout 2 (or ultimate carnage, but UC has GFWL which kills it).

Kind of a driving shoot em up game would be Recoil (tank, boat, hover craft), if you are into that (which I am).

Too bad you already got I'76 though.
Hope it runs for you.

Thank you everyone for more suggestions!

It runs for me, but the colors are a little weird sometimes. I don't think I wasted my money or anything, though.

The best racing games I ever played are

Need for Speed: Porsche
Trackmania Nations (Forever)

Get a 360 and Forza Motorsport 3