I went through half of volume 1 (out of 2 volumes) of FSI's German Basic Course as a complete beginner.
Spaced repetition to great effect. I probably remember every single word from this course. The drills are well-designed, too.
No fluff. The course focuses on learning, and wastes no time on silly tasks and stories.
Clean. I really enjoyed reading the student text (6 MB PDF). It's well-designed and easy to find your way through.
Comprehensive. You practice listening and reading, and grammar and pronunciation are presented in a surprisingly accessible manner. The only missing part is speech skills, which of course can't be taught by this kind of unilateral material.
Alte Rechtschreibung. Spelling has been reformed since this material was written, which makes it unnecessarily confusing.
Specific vocabulary. Most of the words taught are supposed to benefit soldiers stationed around German territory in the 60s.
Some out-dated words and phrases. And you won't know which ones until you use them for real.
It's boring. Unless you're highly motivated, it's hard to stay focused with this course. The most exciting piece of dialogue is "Shall we go down town today?" (Mr. Köhler to Mr. Becker)
The FSI has done a great job distilling language learning into a compact course. If you are a motivated learner, this would be a great resource. Almost all disadvantages come from the course's age. However, that's a real problem, since it takes significant effort to unlearn the old words and old typography.
I'd really, really like to find modern material in the same compact and focused spirit. I haven't found any yet, which is the only reason that I recommend going through this course. Only take the course if intensity and density are your thing and you can't find something more modern.
Please note, though, that you'd want to complement it with a real-life course or a language tandem to practice your pronunciation.
If you are really looking for the quickest way to fluency, move to Germany and study the language full-time for a couple of months, while spending much time with natives.