What I find fascinating is his diversity of style. Had I not taken some art courses in college, I would have never known this.
Most works of artists have all the same style. Once you get familiar with a few of their works, and see a piece that you haven't before, you can call it out. Picasso, on the other hand, went all over the place. Sometimes it's easy to spot a Picasso, other times, you'd never know he created it.
The other thing I like is his intelligent humor. After the Nazi's bombed Guernica, Picasso made a painting (the entire width of his basement), inspired by the event. While living in German-controlled Paris, he was approached by a Nazi officer, and asked, "Did you do this?". Picasso replied, "No, you did."
In a separate event, Picasso was hired to do a portrait of a patron's wife. Expecting a realism piece, the husband saw the cubist result, and was furious. He told Picasso, "That looks nothing like my wife!", and produced a photo of her to show Picasso, "This is my wife!" Picasso replied, "She looks rather small, and flat. No?"