In my experience, some companions seem to be more talkative than others.
Some trigger areas that I have noticed for Imperial companions:
- Tularan Marsh, Taris: a large animal skeleton
- Minimum Security, Belsavis: a hole blown in one of the prison walls
- Gormak Lands, Voss: approaching the giant Gormak cannon
Sometimes the comments totally catch me by surprise. One time on my SW, I walked into Leth Outpost on Hoth and was startled to hear Quinn pipe up with, "I have reinforcements ready if we need them, my lord." Not sure where he was planning on getting said reinforcements, but I guess it's the thought that counts.