"You really can do anything!" This exclamation, from a student in a bead embroidery class, I think sums up quite nicely what I like about it so much. When my co-worker Philonese describes beading as "painting with beads," I feel that bead embroidery is the ultimate expression of that concept.
As someone who designs "on the go" (which I don't actually recommend), bead embroidery allows me the luxury of watching a design evolve. I like being surprised (usually) with the results. If the final piece is less than satisfying, I can always take it apart and re-use the beads -- they never go bad.
Occasionally there's the totally accidental design, as with Leviathan of the Deep Purple Sea.
Since I need to start each embroidery class with "blank slates," as it were, I'll have random buttons glued in advance to some backing. I had been using this backing for a while to demonstrate various techniques. One day I looked at it and thought, "hmm, it's looking kind of like a sea monster." That's when I decided to finish it and give it a name.