Impossible for me to pick just one game. I think the Forza Horizon series and especially 3 & 4 really capture car culture and entertainment perfectly in the same way Top Gear did on TV, the sheer range of racing and driving events is impressive. The Horizon games are the modern version of bedroom wall posters and the car-based TV shows we grew up with. Hotwheels and Lego packs! For that reason, I think they match consoles perfectly, easy to pick up and play for anyone and surprisingly challenging against other good players. It's also worth remembering that Test Drive Unlimited was the real pioneer of the open-world car game, Horizon just refined that.
So many other great games over the years deserve equal mention:
Gran Turismo - those licence tests and buying used cars from the lot.
Colin McRae Rally games - chasing those leaderboard times, so much fun.
WipEout - incredible speed, few can match the adrenaline even today.
Need for Speed - the Autolog where friends times and new challenges would pop up on screen and when you logged in changed almost all racing games afterwards and added so much more competitive fun.
Forza Motorsport series for putting tuning, modifying, car setup and sometimes decent online racing (variable though because the lego brick barriers to enforce track limits were the worst thing they ever did). They drifted the series more towards Horizon and then eventually Turn 10 started to listen and have improved FM7 massively as a result, it's still in the balance to see if they can create something really special with the next iteration.
F1 series for the career mode and including all the real flags and rules of the sport, great on-screen hud to allow access to all the car options.
Wreckfest - ultimately I think Wreckfest is the game that is best matched to console, it's how the majority of console players play most racing games, online lobbies are usually a wrecking competition anyway, at least with Wreckfest that is exactly how it's meant to be. We've had a ton of fun dishing out plenty of car punishment!
Gran Turismo - for surprisingly good if silly racing and those mickey-taking names of the cars.
I'd love a modern remake of Chase HQ too, no one has done that yet!
I've probably missed as many other games that had an influence over the years too, all I know for sure is we've had a huge amount of fun with some racing amazing games!