How many volcanoes are there in the world?

The exact number of volcanoes is unknown. It also depends on the definition of a "volcano": for instance, there are "volcanic fields" that comprise hundreds of individual eruption centers  (such as conder cones, maars, shield volcanoes) that are all relataed to the same magma chamber and that may or not be counted as a single "volcano".
There are probably millions of volcanoes that have been active during the whole lifespan of the earth. During the past 10,000 years, there are about 1500 volcanoes on land that are known to have have been active, while the even larger number of submarine volcanoes is unknown. At present, there are about 600 volcanoes that have had known eruptions during recorded history, while about 50-70 volcanoes are active (erupting) each year. At any given time, there is an average of about 20 volcanoes that are erupting.
For more details, look at what the Smithsonian Institution says about this question.
To see which volcanoes are erupting NOW, look here.