Goldfish should not be kept in bowls.
I cannot stress this enough, and I've practically gone hoarse explaining this to people, so I think I've come up with a good analogy. Bear with me a second here:
Goldfish put out a lot of ammonia, which is a main ingredient in cleaners and urine. (You know how a catbox smells? Yeah. That.) Ammonia is not a particle; most small filters can't touch it (if you even bother to put a filter on a bowl), so it just keeps building up.
Now, imagine living a locked room barely big enough to stretch your legs in. Imagine this room is awash with your own piss. Imagine it getting stronger every day because no one ever cleans it out. Imagine not having eyelids, so you can't close your eyes against the fumes. Imagine having to swallow it with your food, and choke on it in every breath.
Now add a second person...
That's what living in a bowl or a small aquarium (less than ten gallons) is like for a goldfish, and that's why they die so easily. Yes, sometimes goldies are tough enough to stay alive under these conditions...but if you were a goldfish, would you want to?
Of course, this is the point at which some smart-ass always interjects "When I was a kid I kept a goldfish in a bowl for a year, and it was just fine!" Oh yeah? Guess what, bunkie? With room to swim, clean water, and good food (not those trashy "tropical flakes"), goldfish can live up to thirty years and get over a foot long. They are much smarter than other common pet fish like guppies or mollies; they can learn to recognize their owner and actively beg for food and attention. Some even like being petted or held, though too much of that is bad for their scales. One year in a small, smelly purgatory is not living -- it is surviving. It is not the same thing.
Please, don't keep ANY fish in bowls except perhaps bettas -- and then only in large bowls, and only if you research their needs first.