We watch Ponyo at least twice a week in my house (4 year old loves it) and I have always wondered about the boat. The first thing I wondered if a.) it was real and worked - based on jgc's post seems that it does and might be more common than I thought and b.) if the heat would allow Ponyo to actually sit on the top of the boat as she does while it is moving.
Pop pop boats are real and have been around for a long time, I had a couple when I was a kid and it was fun to play with. You can see some more examples of pop pop boats and read some history here: http://www.nmia.com/~vrbass/pop-pop/
The heat from the candle flash-boils the water that's in the "boiler". This is ejected out of the tubing, and once the diaphragm relaxes, it creates a vacuum which pulls more water into the boiler to be boiled again.
The reason it doesn't just jerk back and forth in this exchange is because it sends pressure out in one direction, but draws water in from all directions.
Nice. This design of creating a toy boat has been extremely popular in south east asia for atleast the past 20 years. It's good to see it here again. Nothing beats nostalgia. :)