Goldfish by nature are not aggressive, and are not predatory. The short answer would be, "No, they don't eat each other". However, there are some circumstances where goldfish do eat each other. Goldfish tend to browse for food, eating mostly what are bite-sized morsels, of anything edible. But, if they happen to come across small fish (e.g. baby goldfish), they do not discern, and they will eat it if they can catch it.
At breeding time, goldfish produce hundreds of sticky eggs. Goldfish exhibit no parental care, and they will graze on the eggs, regardless of whether it is theirs. Similarly, those eggs that survive and go on to hatch, the baby goldfish will continue to fall prey to anything that is larger - be it other goldfish, or insects (e.g. dragonfly larvae).
Once goldfish are able to swim around, and are of adequate size (e.g. 2-3 centimeters), the rate of intra-specific predation drops dramatically.
