There have been many sources that I have used in learning Japanese and that continue to challenge my thinking and influence they way I present things at IMABI. Many example sentences are based off of the patterns and teaching methods introduced in these texts.
Japanese Demystified by Eriko Sato: This book was the first book I ever got for Japanese besides a dictionary. The book is well formatted with quizzes and tests. Like IMABI, it limits its lessons to a few set of questions. However, there are some noticeable errors in the text in terms of grammatical classifications, and there are also some odd and costly typos. It is a great place to start out and is equivalent to 25 lessons of IMABI.
Barron's 501 Japanese Verbs: This is a great resource for beginner and intermediate learners that need to see conjugations first hand. IMABI stresses the process of verbal conjugation and uses examples to show them throughout. However, some people just need to see a big chart and tons of examples to have it all sink it. The text has a decent explanation of verbal conjugation at the beginning. However, it does not discuss the bases of verbs. A minus for it. The verbs are also only given one definition, which defeats the purpose for some.
Japanese Step by Step by Gene Nishi: This book has a new edition and has fixed the errors I found in the first edition. It shows the pitch according to Standard Japanese for all words and sentences. This is a good plus. The explanation, though, for many things is just too small. It also doesn't go deep into grammar as near as the first source. However, its honorific coverage is a plus. It lacks a proper index and its discussion about conjugation is a bit watered down to make it fit for anyone I guess.
Japanese Street Slang by Peter Constantine: This book is quite hilarious but seriously shows the many red district terms that define the colloquial speech of Japanese. It is well written and has a lot of footnotes.
Japanese in Action by Jack Seward: It is an older publication but teaches thing with a lot of cultural information with it. It does not a grammar book though. Some things, though, are of an older mindset.
Japanese the Manga Way by Wayne P. Lammers: Love it. The book is big and plenty of room for annotation. The examples for the most part are not corny. There are things I disagree with about the teaching of verbal conjugation, but it is much more accurate on grammatical classification and I agree much more with the Romanization method it implements. It, though, really doesn't talk about honorifics and it is only equivalent to some parts of Beginner's and Intermediate IMABI.
Ultimate Japanese Advanced: Now, my advanced is different from the normal advanced. The text, though, is set up with completely Japanese intros with the chapters studying the grammatical things. Now, this means that things are basically random. Also, you cannot start out with the book because you have to have a decent background in Japanese.
A Dictionary of Japanese Idioms by William de Lange: This book is so helpful when learning about idioms. I had to constantly look at this book when making the idioms lessons. Now, it's translations and entries do get very redundant. Plus, a lot of the entries may not actually be deemed idioms. However, there is a lot to learn from it.
Classical Japanese A Grammar by Haruo Shirane: This man is a god. This book is what made me learn Classical Japanese so quickly, and I hope to one day beat this book in its awesomeness. I may not agree, in hindsight, the placement of certain chapters. Nor does it cover all of Classical Japanese. There are a lot of things that I've learned after the fact and will still do as I prepare IMABI IV.
A Guide to Remembering Japanese Characters by Kenneth G. Henshall: Although it is outdated now, this is the book that made me so proficient in Kanji. There aren't as many examples as it should, and the examples are sometimes very unpractical.
New Japanese-English Character Dictionary by Jack Halpern: This is the best dictionary developed by Jack Halpern. It includes over 3000 characters. Most characters have their stroke orders listed and each character has variants, Chinese form and readings, plus many usages given.