Papua New Guinea gains independence (16/9/1975)

World's most linguistically diverse nation. Crystal says over 800 languages, which is in the right range.
I have to point out that it is outranked by Vanuatu in the per-capita rankings. Vanuatu's languages are all Austronesian, whereas PNG has at least a dozen separate families and some language isolates, so you could say the "depth" of language diversity is greater there.
A while back I looked at the 20 nations listed on this page as having the most languages within their borders.
http://www.vistawide.com/languages/20_countries_most_languages.htm
I also threw in the Solomon Islands, which lie between PNG and Vanuatu.
The top five (plus one) in languages per million population:
Vanuatu   575
PNG   149
(Solomon Islands  125)
Cameroon   17.5
Australia   13.8
Chad   13.5
Languages per million sq.km. area:
Vanuatu   9583
(Solomon Islands  2678)
PNG   1782
Nepal   893
Philippines   600
Cameroon   589
"Most of the languages [in PNG] have very few speakers...." says Crystal. This is a bit misleading. I used to say that all the Pacific island languages were small, as they were well under the mean (7 billion people / 7000 languages = 1 million speakers for an "average" language).
But of course the distribution is logarithmic, and only a small minority of the world's languages have more than a million speakers. The median range of 1,000 - 100,000 represents what I'd call "typical" languages, and lots of Pacific languages fall within that. The largest in PNG are in the hundreds of thousands (e.g. Enga); in Vanuatu everything is on a smaller scale and the top is around 10,000 (e.g. Lenakel).