According to “World’s 18 most endangered spoken languages,” there were 18 languages listed in the UNESCO Atlas of Endangered Languages with only one speaker in April 2010. (Thanks to LoL for the link to this article.)
According to the Atlas, there are now 19, but in many cases, the Ethnologue has different information. The languages listed in the Atlas with only one speaker are (by continent):
Africa
1. Bikya (byb) – the Ethnologue says there are no speakers
2. Bishuo (bwh) – the Ethnologue says there are no speakers
Asia
3. Pazeh (uun) – the Ethnologue says there are no speakers
North America
6. Wintu-Nomlaki, or Wintu (wnw) – the Ethnologue says there are no known native speakers
Oceanian, including Indonesia
8. Lae, or Aribwatsa (laz) – the Ethnologue says there are no speakers
9. Laua (luf) – the Ethnologue says there are no speakers
10. Volow (mlv) – the Ethnologue lists this and Dagmel as dialects, each with one speaker
11. Yarawi, or Suena (sue) – the Ethnologue says there are 3,600 speakers
South America (other than Brazil)
12. Chaná – it appears to not be listed in the Ethnologue (gqn appears to be different); (qs1 – Linguist List code)
13. Pémono, or Mapoyo-Yabarana (pev)
15. Tinigua (tit) – the Ethnologue says there are two speakers
Brazil
18. Diahói, or Parintintín (pah)
19. Kaixána, or Kawishana – it appears to not be listed in the Ethnologue; (qsw – Linguist List code)