So far I have discovered only four: Varric, Bethany, Aveline and Merril. Are there any more?
There are 10: 6 mandatory, 2 optional, and 2 via DLC/Signature Edition.
These companions you get along the way of the main quest line:
These companions require you doing something extra to secure them:
You get these through DLC (or the Signature Edition, which includes some DLC):