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:
Bethany and Carver: acquired at the start of the game
Aveline: acquired during the Prologue
Varric: acquired at the start of Act I
Anders: In Act I, after Tranquility quest
Merrill: In Act I, after Long Way Home quest
These companions require you doing something extra to secure them:
Isabela: Complete Fools Rush In quest
Fenris: Complete A Bitter Pill quest
You get these through DLC (or the Signature Edition, which includes some DLC):
Sebastian: Acquired through The Exiled Prince DLC
Mabari Warhound: Acquired through The Black Emporium DLC. Acts as a fifth party member like Ranger pets did in Dragon Age Origins, not a full-fledged companion.