Initial D: Special Stage is an amazing game. Very arcade-y, with absolutely unrealistic controls, but that's what I like.
As Ghost-Dog mentioned, good drifting skills are the order of the day.
While the arcade mode ("koudou saisoku densetsu") is definitely the core of the game, I like the story mode a lot. I never saw the anime or read the manga, but it was a fun, though seriously cheesy, diversion. One thing to be aware of though: the story is told in voice-overs (from the anime, I guess?) while panels from the manga move onto the screen. This is extremely cool, and a good way to background the game for those of us unfamiliar with the Initial D world, but if you don't understand and read Japanese, it'll be pretty much lost on you.
The story mode actually teaches you important techniques too - first of all, learning to drift well. Certain battles in this mode are useful too - for example, in the battle against Shoji Shingo you race with your hand taped to the steering wheel, limiting your turning. This (if done correctly) shows you lots of good understeer techniques that are crucial to doing well.
When playing the arcade mode, I'd advise you to turn the difficulty down to easy the first time through - if you don't have the system dialed, you'll get owned very early on.
There are a lot of courses too - once you beat the basic offerings (Myogi, Usui, Akagi, Akina, Happougahara, Irohasaka) in arcade mode on both dry and wet surfaces, you open up Shin Myogi, Shin Usui, Shomaru, Momiji Line, and Enna. All of these can be raced in dry and wet conditions in time trial.
There are probably some English FAQs on the car tuning options, so I won't go into that, but basically, you chose tuning "courses" that either give you tuning or parts updates at certain point totals, or later on, allow you to add optional things to your car like new mufflers or spoilers.
Also cool is Iketani's Car Introduction, a kind of in-game FAQ about the various cars on offer, their parts, tunings, etc - good for those of us who are racing game fans, but not car nuts. It goes without saying, though, that this would be pretty much completely lost on someone without Japanese reading ability.
The music is really good, but you'd better like Eurobeat, as that's all that's on offer. Essentially, the music is cheesy as shit, which is fine, because it's fun and works well with the general atmosphere of the game. Unfortunately, there's no volume control that would allow one to change the balance of music relative to sound effects such as engine sounds or tire squeal, which are very loud.
I really, really love this game, and never even played the arcade version or saw the anime. It's just a brilliant racing game that feels like a total labor of love. If you like arcade racing, you owe it to yourself to track this down. However, there is definitely a language barrier - if you read Japanese you'll be fine and will fall in love with the game. If you don't, well, it's not particularly import friendly - I can't imagine it being very easy to negotiate without Japanese skills. Personally, it's my favorite racer in a long time.