Dead, extinct and endangered languages
It is impossible to count all the languages that exist in the world (around 7102 in year 2015 according to Ethnologue), but the sad truth is that more and more languages disappear every single day.
A language dies when the second-last person speaks it dies (as there are no one else to talk to). Extinct languages are those languages that has neither any speakers nor is it used anywhere. Wikipedia has some examples of the extinct languages, like Klallam that used to be spoken in British Columbia or Pazeh, used to be spoken in Taiwan.
In contrast, a dead language can still be used for legal, scientific or religious purposes. Examples of these languages are Latin, Sanskrit or Old Slavic. Some dead languages actively studied, like Egyptian Hieroglyphs or Maya script.
Endangered languages, on the other hand, are those languages that can soon die out. Hopes&Fears on-line magazine made an article about endangered languages, there you can listen to some of the endangered languages. According to Ethnologue, Eastern and Central Siberia, Northern Australia, Central America, and the Northwest Pacific Plateau are those areas that have the highest proportion of the endangered languages. The most common reasons that languages become endangered are natural catastrophes e.g. that can cause famine or flood and by this distinct of a large group of people. These are especially dangerous to indigenous people living in isolated areas. Other common reasons are genocide and language prohibition in a community or a country. Cultural movement, migration and globalization are as well quite common reasons why languages continue to disappear rapidly.
How fast does the process of language-dying happen? Well, according to NBC News, around 90% of the existing languages will disappear in 2050 :(.
The good news is that many international organizations, like UNESCO and EU altogether with governments and linguists are actively working on stabilizing this situation and taking actions to save the languages. These actions include language revitalization and language documentation.