Initial D Fifth Stage

Both shows feature protagonists who although overly excel in their respective fields, still learn new things as new challengers approach. Both shows also have hints of romance and tackle themes such as dreams/future 

The nemesis of this anime is almost the same character 

Um dos poucos animes sobre carros. 

Very strange recommendation, but there's an arc in both where a character, who had previously been under a veil of mystery, had to approach their past and put things behind them, with both of these arcs including fighting an old friend over a woman. This recommendation isn't for the shows as a whole, but how these arcs parallel. They're both incredibly well-written and emotion evoking. I assume more people have seen Bebop, so check out the Initial D franchise if you have the time. 

Fast cars, intense races and a great story! If you like to have a different style and setting, yet want to have an anime focused on the epic race battles, then yes these anime are for you! 

Both involve cars: Tuning them, racing with them, and the like. While Initial D is more about becoming the best racer, Track City is more about saving the world. Oh! Track City's cars are remote-controlled, but that shouldn't matter.