All whales are divided into two large groups of whales, the baleen whales and the toothed whales. Between these two groups, there are a total of about 80 whale species. There used to be many more, but they have gone extinct. For more on whale taxonomy, check out this Wikipedia article:

There areapproximately eighty species of whales.

There are about 65 different species of toothed whales and about 9 different species of baleen whales.