This requires a bit of thought
The current total in the world is about 6800
In the league of current countries the US has 165
Mexico is 2 places ahead with 188
The UK is well behind with just 10
Top of the table is Indonesia with 694
followed by French Guinea with 673

6800 would be the number of "living" languages within the world.....and the numbers you show afterwards are the numbers for each country.....

Prefect answer Lydia! you must have visited the same site I did.
http://www.yourdictionary.com/elr/index.html

actually read it in the Readers Digest some time ago - of course I didn't remember ANY of the numbers, but the basics of your question rang a bell!!!

I seem to remember that India is the country with the most languages, but have no ready source for that. I will check.

India has a diverse list of spoken languages among different groups of people. At least 800 different languages and around 2000 dialects have been identified. - Wikipedia

There are 1652 different languages in India and 350 are recongized as major languages. Most of the languages of India belong to two families, Aryan and Dravidian. - India - Overview

Sir George Grierson's twelve-volume Linguistic Survey of India , published between 1903 and 1923, identified 179 languages and 544 dialects. The 1921 census listed 188 languages and forty-nine dialects. The 1961 census listed 184 "mother tongues," including those with fewer than 10,000 speakers. This census also gave a list of all the names of mother tongues provided by the respondents themselves; the list totals 1,652 names. - This website contains the on-line versions of books previously published in hard copy by the Federal Research Division of the Library of Congress as part of the Country Studies/Area Handbook Series sponsored by the U.S. Department of the Army between 1986 and 1998.