Boiling in and of itself will kill most common water borne illnesses. There are a couple things it doesn't work against, but none that I would really worry about for the purposes of water purification.

[It is worth mentioning, one notable thing standard boiling doesn't kill, is botulism spores. This is one reason why it's important to use a pressure cooker for home canning. While botulism toxin itself is killed by regular boiling, killing the spores requires a greater temperature than simple boiling can produce. A pressure cooker allows for those temperatures (some 250*F), thereby preventing the spores from producing botulism toxin.]