This is probably one of the biggest selling points of The Secret World.
There is a wealth of stories both core to your progression in the game and secondary world expanding level. This is hardly surprising when Ragnar Tourquist of Dreamfall: The Longest Journey fame is at the helm.
What helps push that along further is the fact that much of it is voice acted with cut-scenes so your not sat reading walls of text. Funcom have also learnt from Age of Conan, so this continues well beyond the starter zone.
There really is always something going on that will push you to continue on, which is the sign of both a good story and good gameplay.
For more on the games story check out http://www.thesecretworld.com/gameplay/storyline