I've been using a Stop for a while, along with racks and other descenders. The Stop is great, but may not be the best choice in all situations, as David just mentioned.
Ralph's post talks about teaching beginners to let go rather than grab if they get scared while rappelling. Although I see where he's coming from, I beg to differ. You can't "teach" what is essentially a reflex action. The panic reflex is to grab tight, not to let go. I look at the Stop handle as being more of a convenience than a safety feature. In the rare instance of someone passing out and losing all muscle control - yes, the Stop action should prevent an uncontrolled descent.
I don't think the Stop is the best device to start a beginner on, but it's something that everyone should try at least once. It should be taught like any other descender - grip the rope and control your descent with one hand (usually the right), and keep that hand on the rope at all times when moving! And if you do stop and remove both hands without doing a lock-off, make sure you grip the rope before you grab the handle again.
When you're descending, partially releasing the handle can slow your descent - but that's not what it's designed for! That will pinch and flatten the rope between the bobbins, causing a lot of friction and heat in one spot on the descender and potentially melting/glazing part of the rope. The handle should be used more like the park brake in a car - a safety function applied when you're not in motion.
The previous posts here all make good points about the Stop. It's also discussed more in the On Rope forum under "spinoff post about the stop".