I didn't know that, so I dug around for the cause. From a recent NYP article:

  Takei married his husband in 2008 and Shatner became enraged when 
  he claimed he wasn’t invited. He ranted against Takei in an 
  online interview. [...]

  Shatner called Takei’s wedding a publicity stunt and hypothesized 
  that their feud stemmed from Takei’s unwillingness to playing 
  second fiddle to Shatner on “Star Trek.”

It seems to be mostly based on petty, even comical stuff like this. This may sound paradoxical, but as someone who always had a lot of respect for both of them, this is disappointing and a bit of a relief at the same time.