Which Type combination still exist for which there are no pokemon? With the introduction of Fairy type, the total Types has increased to 18. This has increased number of possibly types (unique, i.e. Primary/Secondary is same as Secondary/Primary) to 171. 

How many of such combinations have been used and which combinations are still left to be used i.e. No pokemon exist for such type?

Examples off the top of my head?
Bug/Dragon, Electric/Poison etc.
Unique Type used in Gen 6 - Water/Fire - Volcanion

Edit: Gen 7 Introduced. Thanks @Kenny980 for updating!
The following image shows the Pokemon types of which there are no Pokemon as of Gen 6:



This information was sourced from: http://bulbapedia.bulbagarden.net/wiki/List_of_type_combinations_by_abundance

--Update for Gen 7-- 

New types that are available in Gen 7:



Which leaves these types still with no Pokemon: