Have you played any of the Shutokou Battle/Tokyo Xtreme Racing/Import Tuner Challenge games? If so, they are definitely worth a look.
What makes them good? Well, they're a rather interesting mixture of racing game, fighting game, and RPG and they feature some of the most addicting gameplay ever.
How do they work? They're basically open world games, where you cruise the highways of Tokyo. Amidst the standard cargo vans and mini-cars of Tokyo traffic, there will periodically be other racers looking for a match. When you see one, you just pull up behind them and flash your brights to challenge them to a race. Which then begins right on the stretch of road you're currently on.
So, how do you win the race? Interestingly, it's *not* by crossing a finish line. Instead, both you and your opponent have "spirit bars" (basically like life bars from fighting games). When one car is ahead, the other car's spirit bar starts to drain. The race is over when one of the racers' bars reaches zero. Also, the bars drain faster as the rivals get farther apart.
Thus, instead of crap like Gran Turismo where you have to spend 20 minutes doing laps around the same track in order to win one race, here races can be over in 60 seconds (or less if you really outclass your opponent). Conversely, if you're closely matched, the races can last a lot longer and feature far more intensity than any other racing game I've played.
Of course, each time you win, you get money to spend on upgrading your car to give yourself the speed to take on the next tier of racers. Oh, and the racers are organized into different gangs with their own personalities and styles (like the Rotary Club, who only drive rotary-engined cars). Once you beat all of the lesser gang members, the gang's boss will appear to challenge you.
It is very easy to stay up very late in the night playing these games, telling yourself "just one more race...".
Import Tuner Challenge is the best looking and has a lot of customization, but, unfortunately, it also has the smallest car selection.
Shutokou Battle 2 probably has the best car selection, and may be a better place to start, even though it's not as pretty as Import Tuner Challenge.