Another fun way to use Random is to get it to make more dramatic changes, but do it less frequently. For example, try creating some synthetic percussion with Operator (or something else, the important thing is that it not be in a Drum Rack so it responds normally to pitch).
Now, program a simple part and set up Random something like this:
This will mostly allow your part to play back as programmed, every now and then inserting a note exactly one octave above or below. Since this setup only generates octaves, it works well for both pitched and unpitched sounds.