I’ve got this great book by Langenscheidt called "Basic German
Vocabulary". It teaches the core 2000 words that are used in 80% of
communication, along with the next group of 2000 words which make up a
further 5%-10%. It also has example sentences for each word.

The words are grouped into categories (Business; Arts; Travel, etc)
and subcategories (Shopping, Work; Music, Film; Street Traffic,
Vehicles, etc), and further split into the core 2000 and the
supplementary 2000. It was the best book I’ve ever seen on learning
another language.

Are there any books that do the same thing for other languages?

If not, are there any websites which feature these words and their
translation into other languages? It would be a bonus if they could be
in a format suitable for use with Vtrain, the vocabulary trainer at:

http://www.paul-raedle.de/vtrain/home.htm

NB - no references to the 100 most common words are necessary. I want
the 2000 and, if possible, the second group of 2000.

What an interesting question!

The Longman Defining Vocabulary is an attempt to condense English down
to 2000 basic "core" words. I am relatively certain this has been done
in languages other than German and English, but haven't found the
proof yet.

In the meantime, these sites about the Longman Defining Vocabulary
might interest you:

http://www.woe.edu.pl/archives/1998/4_98/longman.html

http://www.longman-elt.com/dictionaries/which_dict/ldae.html

Here is the Longman list:

http://www.cs.utexas.edu/users/kbarker/working_notes/ldoce-vocab.html

This one strikes me as somewhat similar, for Japanese:

The Kodansha Kanji Learner's Dictionary
http://www.kanji.org/kanji/dictionaries/learners/learners.htm

It lists the most common 2000 or so kanji (Japanese written
characters), and features several organizational methods (including by
frequency of use, and by subcategories as you've mentioned). Learning
all the kanji in the book would make you about 98% literate in
contemporary Japanese.

I use it at home, and have found it to be a great study tool - kanji
are easy to find, the examples tend to be pretty useful, and I really
like the supplementary materials (like the Category listings, which
group kanji that are like in meaning together).

The Amazon page for the book has some reviews:
http://www.amazon.com/exec/obidos/ASIN/4770023359/ref%3Dcm%5Fmp%5Ffil%5Fall/103-5020910-1011001

Anyway, I hope this helps a bit in your search. Good luck!