Sometimes you don't want to shoot at people in games, sometimes you just want to joy ride and listen to some music. This games are chillaxing in some cases, in other ones you will get an adrenaline rush like no other. This will be mainly arcade racing list with not too realistic driving models. Best example for that is Need For Speed franchise. I probably played most of Need For Speed games out there but will include only one game from that series.
1. Need For Speed: Underground 2
Underground racing games were hot at the time of Fast and Furious first few movies. Underground 2 was the best in that regard. Fully customizable cars that you can make made this game the best for me. Turn on that nitro with "Riders on the Storm" on the radio and be fast.
2. GRID
Grid was more like a simulation with no open world like Need for Speed games. But this game also had that arcade feeling of responsive cars and nice driving feel to it.
3. Flatout 4
Flatout game are more destructive in nature. You could drive from buggies to trucks and all sorts of demolition derbies. Cars would loose the parts from all that destruction. Fun game.
4. Carmageddon 2
Most brutal driving game on this list. Wreck other cars and run over everything to get extra points. Not your typical driving game but it was about driving, kinda.
5. Driver
Not your typical driving game, this one had a story where you drive around and help criminals escape the police. Driving model was great, to this day one of the most fun games I've played.
6. Rollcage
This game was crazy. You had a double sided car that could flip on both sides and do all kinds of crazy moves. Very fast speed and weapons included to beat you opponents.
7. Burnout: Paradise
Open world with great crash physics where you can just drive around and be destructive. At the time one of the best graphics and physics in racing game.
8. DIRT 3
Codemasters made a nice game from DIRT 3 with different kind of stuns to do. Fun and creative with nice graphics.
9. Trackmania Nations
Trackmania is full arcade racing game, tracks can have many big jumps, loops, flips, crazy nitro moves. You can even create your tracks for online play.
10. Fuel
This was more of the open world of road game with customizable buggies and quad bikes. Nice graphics and jumping physics.
