Aquarium keeping is not as simple as it looks. A fish in a bowl is not going to have a good time. If you are suffering from mysterious deaths, and you're just getting started, check out the following links.
First, a concise, bare-bones guide to keeping you fish healthy:
Basic Fish Keeping (http://www.petfish.net/kb/6/)
Second, EVERYTHING you need to know to get your fish going:
Beginner's FAQ from thekrib.com ( http://faq.thekrib.com/begin.html)
I recommend that everyone, beginner to expert, problems or not, read through this.
If you know that none of the basic problems outlined here are afflicting you fish, look closely for any signs of parasitism. Lethargy and quickly beating gills are common. Check to make sure no artificial chemicals, like Windex or perfume, could have entered the tank.
