Minecraft-like game I wrote with my daughter. I discovered their use the hard way after having suffered through without them. Any time you are freely rotating a viewpoint or an object in 3D space, you will probably want quaternions.

Do write some good test cases though that compare to someone else's implementation. I accidentally wrote my multiplication backwards and didn't catch it for a long time. I just had a vague feeling that something was wrong every time I wrote rotation code.