Reasons I love it when the kids play by themselves:

1. It's healthy for them: solo play builds a child's self-confidence and self-reliance, strengthens their sense of individuality, provides an outlet for ideas and emotions that otherwise haven't found acceptable expression, helps them learn to focus and builds their attention spans, and can even sneak in some lessons in observable science and math.
2. I get to witness their imaginations in action. Alex is still a little too young yet to really "play pretend" but Penny's eyes see into the most amazing worlds, and her brain concocts fantastic stories: A bunch mermaid sisters are trapped by an evil wizard and have to trick him to win free! Wonder Woman and Batman are fighting bad guys!
3. I also get glimpses into their growing and ever-changing personalities. Penny is family-oriented nearly to the point of obsession. Even when she's playing with her superheroes, there is always a daddy or a mommy. Alex is much more into exploration and experimentation. He's much more patient with trial-and-error than Penny was at the same age (or even than Penny is now, for that matter). He's also an extremely active learner. Even while playing by himself, he frequently seeks an adult's confirmation that he's got the right word for something, or the right color, or wants to count items, or name the letters... Sometimes all in the same 5 minutes. Just now, for example: "Heart? Heart? Red heart! Pu'ple heart! Count hearts? One! Two! Three! Four! Five! Eight!" (He has trouble remembering that six comes after five, but if reminded, can get to about twelve without other errors. Which I think is pretty darned good for a two-year-old.)
4. I get to be lazy, just watching and occasionally responding to prompts to admire their efforts. Sometimes, it even gives me time to do other things -- like write blog entries.