If an egg is bad, it floats in fresh cold water. If an egg is good, it sinks. You may have dismissed this tip as nonsense, but there's some solid science behind it, according to the USDA.
While egg shells seem solid, they're actually slightly porous. As an egg ages, a sac of air begins to form inside around the inside of the shell. The older it is, the more air becomes trapped inside. Once there is so much air inside the egg that it floats, chances are it's gone bad (of course, an old egg can still be OK to eat, but better safe than sorry!). Fresh eggs, on the other hand, will sink to the bottom of a bowl of water.