there's nothing better than carmageddon 2

Hopefully Star Wars Episode 1 Racer will appear here one day. Apart from that the three best racing games I've ever played, or at least, games with racing in them: NFS:Most Wanted, Test Drive Unlimted and GTA 3 : SA.

Driver San Francisco. It has an actual story and characters, not a very serious one surely, it's more like an extra crazy episode of a 70's cop show.

You play as the dream of a cop in a coma, and in it you can possess any driver on the road, while doing that you come across different missions involving those people and you usually solve them by driving really fast, like the one about the kid in an illegal street race trying to get money to pay for college, or another kid in their driving test with a berating instructor and you drive so dangerously he poops his pants.

There's also several missions based on classic movie chases. I'm not a fan of racing games, but this one had so much personality that I loved it.

If you have also PS3 go for Gran Turismo 5 and 6. On PC there is also very good Assetto Corsa and Project Cars. And on Xbox Forza Motorsport series. I can recommend to you to try all of them.

This one!
Remarkable game, runs prettty smooth on PCSX2, too! Go for it, you won't regret it.

Runner ups: PGR series / Auto Modellista / Tokyo Xtreme Racer/ Kinetica ;)

Richard Burns Rally (RIP). But it's only for rally heads who are into realistic driving. To play that game effectively imo you need a dedicated station with a high quality steering wheel, which I simply have no space for. Although playing it without power steering gives you a really good arm workout.

For now I've been playing Horizon Chase on my phone.

How much would you be willing to pay for a good wheel? And would you ever consider a "basic" [e.g. no force feedback and possibly limited too, say, 360 degrees?] wheel if it were cheap enough but well built -- as in sturdy and reliable?

I got Richard Burns Rally this year and it's amazing. But I don't have a wheel. I try playing with a gamepad, but frankly it's quite hard. Even though you can adjust the input response curve and everything in RBR, I still can't find a setup where a gamepad's stick is precise enough for small adjustments at high speed and at the same time fast enough for tight cornering... and in such a game, even very small mistakes can end up very costly.

I contemplate buying a wheel, but the "consumer level" is dominated by Logitech [followed by Thrustmaster] with a wheel that is both way too expensive for what it is (imho; it's just a pile of plastic with two cheap wimpy brushed motors, an encoder, a few buttons, usb interface...) and at the same time lacking in features and quality. I almost caved in and bought one but then I got to try one at a local store and wow, that thing really feels like a shitty cheap toy. AIUI the Thrustmaster offering isn't that much better, you just make different tradeoffs.

Starting today, I'm out of a job. For a long time now, I've been considering making a startup. Also, for a long time now, I've been considering making my own wheel... 1+1? I firmly believe it's possible, and not even that difficult, to make a wheel that's both better and cheaper than the Logitech offering. At the same time, I think there are lots of people who would fall into love with racing games even with a much cheaper "basic" wheel that still gives you a significant precision & speed advantage over a gamepad (actually such wheels do/did exist but they're a bit too cheap, basically toys that go out of calibration and can't take any abuse and probably lack the buttons you need to interact with your game). I think it should be possible to offer that in the price range of the official playstation gamepads.

Yes, the problem with wheel sets is that if you want a really good one it will be quite costly, at least €300.
The other problem is they are usually limited to one or two systems: PC + PlayStation, PC + Xbox, Ps3/4 etc.

I would say that you don't get a good one for 300 eur (and yes that's still expensive). You get a mass produced toy that's engineered to be about as cheap to produce as possible, and then a ton of marketing to make it appear like a top product (in a market that really lacks competition, unfortunately). Like with many other gaming peripherals today. It's a race to the bottom, very similar to the situation with gaming mice that are expensive and have lots of buttons and blinky leds and a bazillion (advertised) DPI and that break in a year or two because everything is as cheap as it can be, and the marketing is there to make it appear premium.

In the two 300 eur range wheels, you get to choose between a quiet belt drive or a rattling gear drive with two dirt cheap wimpy brushed motors that short their slip rings in a year or two of heavy use.. you get a set of pedals with no clutch (what the f**k, why would you ever sell a clutchless set as your top end offering for racing fans?) or a set that juts has poor response (worse than a previous model because they went for a cheaper build, while hiking the price...). You get an optional low quality shifter (for 60eur or something like that) and it randomly fails to get in gear even though the stick is in the right position. Shit like that. A very simple product and still so poorly designed you can't rely on it...

These aren't good products, but these are expensive and the best the average gamer is going to find when they first look for a set to buy. It's depressing. And then they think it's good or "the best" because it was so expensive, despite obvious flaws.

There are much better products out there, but they're mainly built by & for sim enthusiasts [individuals or small companies] and are ridiculously expensive. Many of these show real lack of engineering, which reflects in the price. So you get a $500 to $1000 motor (plus controlling power electronics) to give about as much torque as you can get from a $60 battery powered drill driver. Yeah it's nice and quiet and it works, great for the serious enthusiast who doesn't care about all the money and space spent. Not good for most of us.

My last wheel was a Fanatec Porsche Wheel (see attachement) which costed me new 300 euro 3 years ago, I sold it last week for less than half that.
It's in the same pricerange as a Logitech G27 but has better pedals and force feedback whereas the G27 has better production values. I also had a DFGT but it broke after less than a year and I even consider it better than the cheapo Thrustmaster wheels which are godawful IMO.

After a while I didn't use my wheel anymore because of the continued rebuilding of my desk and my seat postion wasn't good so I needed to lift my left foot so it doesn't rest on the clutch/brake, which gave me stomachache.
Unless you go for a setup where you can sit like you're in a car I wouldn't even consider buying a wheel and happily stick with the gamepad.

Since there are enough enthausiast willing to pay a lot of money for wheels+pedals these things cost a lot (new), even Fanatec ditched their relative low budget stuff and now the cheapest set will cost you over 1k euro.
Logitech's new wheels look nice though.

As for DIY wheel, do you have an example or tutorial? Because building a force feedback wheel is already quite challenging but you also need to have software to hook it up to the computer, maybe you could use Logitech/Thrusmaster/Fanatec drivers by using a donor wheel.
Sounds like you're putting too much torque on the wheels and need to ease on the throttle so the car will be less nervous when making steering inputs.

Someone already mentioned Burnout Paradise, So I'll just throw Need For Speed: Most Wanted out there. Is it the best racing game or even NFS game ever? I wouldn't know, I just know that I played it to death many years ago and loved it! Please mind that I am talking about the 2005 version and not the one that came out in 2012.

I would also be interested in racing games, namely HORSE racing. Any tips? All I have seen so far have been on the wrong side of mediocre.

I know horse racing games used to be common in arcades, more so in Japan than in the west though. But sadly I can't think of any spesific ones right now, but if you go look around for arcade games you are bound to find some.

I use a Logitech Rumblepad 2, which I think is the best gamepad ever made, especially for racing because of its squared axis limits means you know when you reached the maximum limit.
I use the old layout used for RC cars, which is leftstick=throttle/brake, steer with the rightstick and shift gears with the shoulderbuttons. With the game or the controller software give the throttle/brake and steering axis a 5-10% deadzone and give the steering a sensitivity of 25% or less.
As for holding the gamepad, don't hold it on your desk but rest your hands on your lap, which never gave me issues.
You can use a button so you can brake while applying throttle (or the opposite) but I haven't bothered to do this yet.
I see, nice.
https://www.youtube.com/watch?v=sdmsRcsl_xA