Is there a data source for annual global precipitation?
In case you want to learn something about precipitation first:

http://www.nasa.gov/mission_pages/GPM/main/index.html

There is the most important information about current missions with some videos, too.
If you click on the education link a little lower on the page you can learn a lot about how the data is retrieved and about earth's water cycle itself.. if that's not interesting to you and you just want the data this here is the right way:

http://giovanni.sci.gsfc.nasa.gov/giovanni/

The site does not just provide data about precipitation but about all measurements that are made from space such as amounts of aerosols, evaporation rates, heat flux, vegetation, wind speed and so on.. you'll see it all on the left site of the page.. just make a tick on the dataset you need and all measurements will pop up on the middle of the screen, make another tick on the information that suits your needs, choose the time span you wish and the area of the map you want to know more about under "show map".. if you're done with that just click "Plot data" on the right bottom corner and a map with the data you wish will show up.

I hope that helps!