The reason why Turkish is in the same group as Japanese is probably because of the subject-object-verb [1] order they have in common (vs SVO in English). This is why even spoken Japanese is difficult to master for English speaking people.
Turkish (not just the language spoken in Turkey but spoken on a large swatch of Asia, including Kazak, Ozbek, etc.) was perviously grouped with Korean, Japanese and some other local languages as the Altaic group. They are quite similar. This grouping is no longer widely accepted. I've read that Japanese academics want their language to be treated as an isolate and certainly not grouped with, e.g. Korean, because of nationalistic reasons.
[1] http://en.wikipedia.org/wiki/Subject–object–verb