Japanese for Busy People (kana version)
These books are simple and logical, with good English explanations of the points covered in each lesson. The language used is appropriate for business people, so may be less appropriate for you, depending on what you want to learn Japanese for. The kana versions are far superior to the romaji versions. You have to learn kana anyway, and it’s not hard, so why not start from the beginning? Volume 1 uses hardly any kanji, but volume II introduces a dozen or so with each lesson. Useful for recognition, but you’ll need a proper kanji book to learn them properly.
Volume III is also available, aiming to bring you up to a solid intermediate level. I have also used the Japanese for Busy People workbooks and cassette tapes to support the books. They are worthwhile but not at all essential. CDs and other accessories are also available.
This series is quite popular. My Japanese classes here in Japan use it. You can buy them at Amazon.com. If you’re in Europe, go to Amazon.co.uk