I tend to use a logic analyser most because a lot of my work is digital. But with my current work designing voltage boosting power supplies with a flyback transformer, digital analysis just won't cut it. The multimeter doesn't get me very far either.
I'd use the Oscilloscope to confirm timing and current modes of my design. At least three channels would be best for this, so a 4-ch scope is ideal. Of course, there are many other applications this would be used for.