Textbooks:
Genki, which Goldenspines mentioned, is good; I use a different series, called
Minna no Nihongo, which is about on par with
Genki. For each level you do have to buy two books, though: the workbook and a separate book of English translations (of the dialogues, etc.) and grammar explanations. I'm not sure which physical book is cheaper. However, the
Genki textbook has quite a few exercises that you can do online for free.
[url=iknow.jp]iknow.jp[/url] is definitely excellent—their vocabulary sets are based on the most common words in the Japanese language, and that in itself is invaluable. It also keeps track of your practice so that you review words that you missed more frequently and review all words with decreasing frequency as time goes on, which is ideal for long-term retention. It’s just too bad that it’s not free anymore.
Although the name sounds silly,
Slime Forest Adventure is a resource that I used a lot when I first started learning Japanese; you can learn hiragana, katakana, and the first 500 kanji, or however many the game includes (meanings only, no readings). It really is a good source for fast, repetitive drill; I’d particularly recommend it if you haven’t learned hiragana and katakana yet. Like many of the best language resources, it will drill you more often on items that you miss than on items that you consistently get right. Apparently there’s a free version and a paid version, but at $10 the paid version is not expensive.
Everything below is a free service:
http://www.renshuu.org has tons of resources for practicing vocabulary, kanji, and grammar. You can use it to study according to what is on the JLPT or Kanji Kentei tests; there are also some textbook lessons. Also, it has a really neat feature where you can choose the format of the question and answer, so you can practice both receptively and expressively: for example, you can choose to see a Japanese vocabulary word written in kana as the question and practice whether you know its English meaning, or you can do the opposite, see the English term, and practice coming up with the Japanese equivalent. Or for anything that includes kanji, you can practice readings (whether you know how it is pronounced in Japanese).
http://kanji.koohii.com/ is a good site for learning the meanings of kanji using mnemonics. In that regard, it’s a good substitute for books like Heisig's
Remembering the Kanji or Henshall's
A Guide to Remembering Japanese Characters. (The Henshall is a great book, by the way!) However, it
only has drills for the English meanings of kanji and will not help you remember kanji readings (the on-yomi and kun-yomi).
For getting information on specific kanji, [url]japanese.about.com[/url] has surprisingly good pages on kanji, indexed by
grade level or by
reading. They also have a bunch of other resources I haven’t looked through. But I like their kanji pages because for each kanji they give the stroke order, list the on-yomi and kun-yomi, show which radicals the kanji is made of, and give examples of kanji compounds that use that kanji character. All of the readings and compounds are given both in kana and in romaji (though I can't imagine why someone studying kanji would not be able to read hiragana and katakana). Somewhere or other on the japanese.about.com site there are also pages where you can view the stroke order of hiragana and katakana, which is helpful if you want to be able to write.
Anki is a flash card program free to download to your computer, and it is very customizable. This is great for any language, really, not necessarily just for Japanese. It will also keep track of your progress, drill you more frequently on words you have missed and less frequently on words that you got right easily, and taper off practice so that you practice a word frequently at first and less frequently as time goes on.
My Language Exchange is another resource that’s for any language, not just Japanese. I haven’t used it and can’t vouch for it personally, but it’s a free service that will pair you with a native speaker in your target language who wants to learn to speak your native language. You will spend half your time conversing in your target language and half of it conversing in English; there are some reasons why even the time you spend speaking in English is helpful, which the website explains.