The only thing I've used a router for so far is to round-over corners and my failed attempts with a dovetail jig. I avoid using my old Craftsman router and don't care for the base on my Ryobi. A Dremel seems like a poor choice for cutting circles and I'm too much of a perfectionist to use a jigsaw.
To test an idea I had, I made a circle jig outta scrap plywood with a nail for the center and a pilot hole for the radius of the circle. I nailed one end to the circle's center, stuck my Dremel in the pilot hole and proceded to cut the circle out. It seemed to work pretty well, but the bit started to enlarge the pilot hole and drift a bit. I new that was gonna happen eventually. just before the end of the cut, with 2" to go, the bit snapped on me. My guess is from too much angular pressure from it wobbling in the jig.
Has anybody else used anything but a jigsaw or router to cut circles and stuff?