Any books that can help you learn Japanese? Also, any books that teach you about Japanese culture and history?

What level do you want to reach?
(base on 4 hours per week)
For beginner level, between 3 months to 2 years
For Intermediate level, at least 3 years.
For Advanced, more than 4 years.

Books: Genki 1 and 2 (Beginner)
An Integrated Approach to Intermidiate Japanese

For westerner, I recommend "Nakama" textbooks because they give you kanji pratices, culture and many English explainations for phrases...

"Japanese for busy people" is also good for westener, but I think it is not intense enough.

Too vague of a question to answer. What do you mean by learn? Know how to say "hello" and "goodbye"? Be able to read books? Be able to watch movies? Be able to carry conversations? Be able to discuss difficult topics? Be able to translate? These are all very different skills. Language is not something you just read a book about and suddenly you can read/write/hear/speak it.
Imagine basketball. If I spent 3 hours a day shooting three point shots for a year, I'd be great at it, but would I be a great basketball player? Probably not. Language is the same. So, tell me what your specific goal is, and I'll be able to answer your main question.
Also, for learning Japanese, I highly recommend A Dictionary of Beginner Japanese Grammar. Tons of practical, easy to use grammar points that will help you no matter what level, and lots of easy explanations. I personally don't like learning "conversational" Japanese from textbooks, but the Japanese for Busy People series seems popular. Any little kids books are good for picking up hiragana and katakana, and if you get good enough, I highly recommend manga (especially Doraemon and Detective Conan at first, but whatever suits your fancy works great). A great way to see natural Japanese in action and pick up some vocab. Kids' shows are an excellent way to build learning skills and fundamental vocab.
As far as Japanese culture... I haven't read too many books on the subject, but I liked "The Japanese have a word for it". Besides some esoteric vocab, it gives a bit of perspective on Japanese mannerisms and culture, although it's kinda on the business slant.

do you want to learn japanese because you like anime? just curious..anyways, there are a lot of books on the japanese language and culture. I believe if you really wanted to learn it and studied everyday..you could learn it in a few years. Japanese basics are easy but writing and speaking sentences are hard. i recommend buying a japanese/english dictionary. Watch movies in japanese with english subtitles.