From Daytona USA to Time Crisis 3, this game stood out when I was young: Thrill Drive, specifically 2.
Thrill Drive is like Burnout, except with a conventional car list. Unlike Burnout, Thrill Drive focused more on road safety. As seen in the car selection menu, loads of road signs fill out the background. Also, the in-game HUD has some sort of chart evaluating your driving style. Screams were added when you crash for that added fear factor. I pretty much hear that many times because I always intentionally crash.
Check out this gameplay from the arcade. I wish I can find a cabinet for this (because from the videos I've watched, controls don't work in emulators.