With a proper mod and ufo extender accuracy, I find Heavy Cannons to be quite useful in the early game. Aim at the floor in front of an alien to create a descending shot or at a wall nearby and you will be very likely to create an explosion near enough to kill it, much better than missing by a hair's width with direct fire. It also kills reapers in 1-2 shots for those floater terrors. Without extender accuracy, the auto-cannon is probably better, but with it and a reasonable tweak (making the heavy cannon more accurate at range and the auto-cannon focus more on the auto-fire), they can both be very useful.
Obviously, by the time you have laser weapons, it becomes less useful, and is totally irrelevant when you get plasma. So the question is confusing, as Solarius said. How often do I use Heavy Cannons? A lot in the early game, a little mid game, not at all end game. Do I value it as a weapon in the game? Certainly.