Inconsistent timings of world championships According to Wikipedia recent world championship tournaments have been played in these years:

2006 
2007
2008
2010
2012
2013
2014
2016    

What is logic behind this, sometimes they are played every year and some there is gap of year? I can't find explanation for this inconsistency. Why wont there be game in 2015?
Due to funding and other problems with FIDE, the world championship schedule has been changed many times during past few years. TLDR: After the title reunification match in 2006, there was a tournament in 2007, followed by matches in every two years, starting from 2008. The 2013 match was an exception.

The match in 2006 was the reunification match between the FIDE world champion (decided in knockout tournaments by FIDE) Topalov and the classical world champion (decided by matches against the current classical world champion) Kramnik. Before the match, FIDE had announced that there is a world championship tournament in 2007. Kramnik and Topalov agreed to that. Before the 2007 tournament, there was also an agreement that if Kramnik (2006 winner) does not win, the winner of 2007 tournament needs to play against him in a match in 2008. 

After that match, FIDE had decided to have a 2-year world championship cycle. However, there were some problems with some players withdrawing from the qualification tournaments because rule changes by FIDE, see e.g. the list in Wikipedia's page on the 2012 match or Carlsen's interview. FIDE apparently reacted to that and shortened the world championship cycle: the qualification cycle for the 2012 match started in 2008, and the qualification cycle for the 2013 match started in 2011. 

As to when it was decided that there are matches in both 2013 and 2014, my memory fails me. The lists in Chessbase and FIDE web site, both dated on March 28th 2012, are different. The FIDE contract with Agon in early 2012 might also have something to do with it.