It depends on who is counting and how they count them. SIL International’s Ethnologue detailed a current list of 7,102 distinct languages. Of those, they consider 578 “Institutional” languages (well-established international, national or regional languages). This constitutes the top 8% of world languages, but represents the vast majority of global population. Another 1,598 languages (22.5% of the total) are “Developing” (standardized and modernizing, with broadly-established literature). A further 2,479 (35%) are “Vigorous” (used daily by all generations in a society).
Two more categories show how some languages are in decline: 1,531 (21.5%) are listed as “In Trouble,” and 916 (13%) are described by Ethnologue as “Dying.” Those languages that are “In Trouble” are still spoken by adults (parents or the elderly) but the language is not being transmitted to younger generations. Those that are “Dying” are only spoken by the elderly. Not even the child-bearing generation is fluent in their traditional language.
While languages are indeed dying, the number of recorded languages spoken in the world has mainly increased over recent years. For example, the 1996 edition of the Ethnologue catalogue listed 6,703 living languages. That number increased to 6,783 in 1990, and again to 6,912 in 2005. However, it dropped back to 6,909 in the 2009 edition. It rose again significantly to 7,105 (or 7,106) in the 2013-2014 17th Edition before achieving the current level of 7,102. Many of the increases were due greater distinguishing of what constituted a language. The decreases were due to linguistic extinction.
Now that you know a few of the official numbers from Ethnologue and Glottolog, try to sit with a pen and paper and see how many languages you can list! (And no peeking at the listings!) Can you get over a hundred?