I don't really read mangas.... The Art style in combination with the lack of colours is sometimes to hard to follow, so it gives me a headache. Not to mention Right to left Reading.
As for anime.... I could put my entire list here, but that'd probably be a very bad Idea, so i'll just name a few off the bat.
My Favorite non-car animes
A Certain Scientific Railgun, overal my favorite comedy/action anime Misaka is Kawaii, and there's a 100+ Clones, so yeah, big plus there
Clannad and also Kanon (I cri evritiem, these are very sad, but very well written stories, not the best music lyrics though)
Girls Und Panzer (Tanks don't count as cars, and watching this is simply hilarious)
Accel World and Sword Art Online (Both of these involve a Virtual gaming world and a story revolving around them)
That's a few. I have atleast 50 more i've finished watching, and hundreds more that i need to watch.
As for Car Related Animes.
This has to be my favorite car-related anime.
Mainly because I think this anime could well be predicting the future.
Let me just get a part of the story:
"In the distant future people no longer drive cars themselves, instead relying on AI (artificial intelligence)
computers to drive their cars for them. But when these AI systems start
losing control and running wild somebody has to stop them. éX-Drivers
are the people who are able to operate the older mechanical non-AI
dependent cars who chase down the AI cars and stop them."
This sounds to me like that could be reality in the near future.
And for other car related animes.
Initial D and Wangan Midnight of course.
You're under arrest is one i still need to watch. The Protagonists drive a Honda Today Police car.
Gunsmith Cats (And the Older Riding Bean) are also nice car-related action animes.