There are 7 species and one subspecies:

Mute Swan (orange beak) England, Eurasia

Whooper Swan (yellow/black beak) National Bird of Finland

Trumpeter Swan (black beak) North America

Tundra Swan (black beak with small yellow lore-space between beak and eye) North America

Black Swan (black swan with red beak) Australia/New Zealand

Black-Neck Swan (most fragile species, black neck/white bird with large caruncle on beak). South America

Coscoroba (smallest swan that looks like goose, duck and swan, white with pink/coral beak and feet). South America

Bewick Swan (yellow/black beak) Eurasia Sub-species of Tundra Swan

As far as populations, you will need to check with the various areas that the swans are native to determine approximate numbers. Another issue is that many of these species are also kept in private settings, zoos, etc., and population would have to also consider these collections.

Interestingly, at one time in their existence, all swan species were listed on endangered species lists due to the feather trade, hunting, lead poisoning or other issues that decimated their numbers. Many countries and environmental entities worked to bring populations back. Now, many of these same areas are allowing the culling of populations.
The Regal Swan