Can You Float A Planet?
It seems the answer is “Yes.” Not too long ago planet searchers have discovered something they gave the unlikely name of TrES-4. This planet is a gas giant like Jupiter. In fact it has five times the volume of our nearby neighbor. However the mass (as determined by the planet’s interaction with its sun) has been determined to be only about 80% of Jupiter. Five times the volume, 80% of the mass. If you do the math it turns out that this planet would float on water.
All we need is a 151,000-mile-wide body of water to perform that experiment. 
The planet has its own wiki page where it is further described as a “puffy planet” because of it’s size to weight ratio. There are quite a few planets that have been discovered outside our solar system (exoplanets) over the past decade or so, and the rate of discovery is certain to increase as our understanding of both the technology required and the best places to look improves. I can only imagine the public interest that will occur when the first earth-like planet is discovered.