I still fire up the 360 arcade remake OutRun Online Arcade every once in a while. It has a charm that really appeals to my boyhood dreams and I don't care if the game offends anyone. Unfortunately I think Ferrari pulled the license after it lapsed so it isn't for sale anymore.
Arcade racing games
I well try to mention some games that have not already been listed. Thanks to the other posters for highlighting some games I didn't know.
I love Test Drive Unlimited because you could buy cars and garages on a life size (I guess) replica of Hawaii. It was a ground breaking open world driving game (before Burnout Paradise I might add). The sequel Test Drive Unlimited 2 was slightly disappointing because the first one was so great but I enjoyed it anyways (truly unique exotic cars that you can test drive, buy and customize). Unfortunately it probably didn't sell well because the studio closed.
Just the humor and Douchie McBrotag main character make me want to stay far from this game. Got a feeling that this will tank, regardless of reviews.
You do know that you can play as a female protagonist as well?
I don't have an Xbox One (or PS4) but this game looks like a breath of fresh air for those of us who don't find pleasure in melodramatic melancholic shooters like Gears of War or Metro. The more good games to choose from the better IMO.