Wikipedia maintains a list of mammalian species which are classified as possibly extinct. The list currently runs to more than 20 species which are presumed to have become extinct in the last 100 years or so.

But the verification is problematic - occasionally 'extinct' species re-appear ^{[Ref. Needed]}

If it were necessary to be absolutely certain that a loss had occurred before it could be counted, the list of modern-era extinctions would be very short indeed. This is the major reason that extinction rates are usually estimated by proxy measures, such as the one that relates annual loss of rain forest to some calculation of species richness (for an extended discussion, see May et al., 1995). The trouble is that proxy estimates are difficult to verify and can lead to rate estimates of enormous magnitude (see Brooks et al., 1997).

Source :"Requiem Æternam: the last five hundred years of mammalian species extinctions". In MacPhee, Ross D. E.; Sues, Hans-Dieter (eds.). Extinctions in Near Time. Advances in Vertebrate Paleobiology.

Note: This article refers only to mammalian species, by way of example, to demonstrate one of the many unknown factors encountered when trying to quantify the Number of Speciesplugin-autotooltip__plain plugin-autotooltip_bigNumber of species

"We demonstrate that after more than six decades, estimates of global species richness have failed to converge, remain highly uncertain, and in many cases, are logically inconsistent."

Source : Global species richness estimates have not converged for Trends in Ecology & Evolution.