That's like asking how many Cartoons exist in the world. There's more and more anime being created every day, so there's really no way to tell.
There are two seasons for the anime Free as of summer 2015's anime season.
http://www.theanimesuperstore.com has over 800 anime series
The anime series "Monster" has 74 episodes .
Currently, there are none. But there is an anime TV series on Cartoon Network.
The anime series "Spiral" has 25 episodes .
An anime series does not of necessity start with manga . Manga usually generates enough interest to spawn an anime series ; the two are not mutually exclusive .
The anime series "My-HiME" has 26 episodes .
The anime series "Tactics" has 25 episodes .
Now and then,here and there . Is a very good anime series .
There is already an anime series for Hanamaru Kindergarten.
The anime series "School Days" has 12 episodes .
The anime series "Burst Angel" anime series is a Shoujo-Ai , or Yuri , based on lesbian themes .
The anime series 'Kamichu!' has 16 episodes .
The anime series Inuyasha has 167 episodes .
http://www.theanimesuperstore.com has over 800 anime series
Yes , 'X' the anime series has 24 episodes .
There are 114 episodes of the anime series 'Saint Seiya' .
There are many, but Inuyasha is a long running anime with fighting and romance.