I know that boiling does little to break down chemical contaminants or heavy metals. But I'm unsure if it kills all microbial life. Are there any waterborne illness-causing viruses/bacteria/protozoa/cysts that can survive boiling? And if so, how serious is the illness they cause?
This article (*) gives a good summary of the efficiency of boiling as a method for making water safe for consumption. In particular, Table 2 provides a summary of the temperature and time required to kill various micro-organisms.
Sterilisation of water (killing all living containments) is not necessary to make water safe to drink. For example, boiling may not be effective against bacterial spores such as Clostridium which can survive at 100°C (212°F), however, as Clostridium is not a waterborne enteric (intestinal) pathogen, ingestion will not cause infection.
All waterborne enteric pathogens are quickly killed above 60°C (140°F), therefore, although boiling is not necessary to make the water safe to drink, the time taken to heat the water to boiling is usually sufficient to reduce pathogens to safe levels. Allowing the boiled water to cool slowly will also extend the exposure of waterborne enteric pathogens to lethal temperatures.
Boiling also gives a simple visual indicator that a high enough temperature has been reached when a thermometer is not available.
(*) Backer, H. Water Disinfection for International and Wilderness Traveler. Clinical Infectious Diseases. (2002) 34 (3): 355-364. Available from: http://cid.oxfordjournals.org/content/34/3/355.full
Boiling kills everything -- giardia, cryptosporidium, other bacteria, and viruses. 185°F (85°C) for a few minutes will do it, and boiling for one minute will do it. (Boiling is lots of big bubbles, not just a few small bubbles on the side of the pot.)
Some people recommend longer boiling times at higher altitudes because water boils at cooler temperatures there.
(Source: Wilderness Medical Society, The Backpacker's Field Manual by Curtis)
Botulinum toxin is particularly tough, as is Bacillus cereus. B. cereus is more likely found while camping.
But your goal is not so much to kill everything as reduce the level to the point where it does no harm. The dust you breathe, the things you touch, and (yick!) the people you are with all bring various pathogens, as does your tap water and (often especially) bottled water. Do your best, and your body takes care of the rest.
The elimination of micro-organisms by boiling follows first-order kinetics—at high temperatures it is achieved in less time and at lower temperatures, in more time. The heat sensitivity of micro-organisms varies, at 70 °C (158 °F), Giardia species (causes Giardiasis) can take ten minutes for complete inactivation, most intestine affecting microbes and E. coli (gastroenteritis) take less than a minute; at boiling point, Vibrio cholerae (cholera) takes ten seconds and hepatitis A virus (causes the symptom of jaundice), one minute. Boiling does not ensure the elimination of all micro-organisms; the bacterial spores Clostridium can survive at 100 °C (212 °F) but are not water-borne or intestine affecting. Thus for human health, complete sterilization of water is not required.
The traditional advice of boiling water for ten minutes is mainly for additional safety, since microbes start getting eliminated at temperatures greater than 60 °C (140 °F) and bringing it to its boiling point is also a useful indication that can be seen without the help of a thermometer, and by this time, the water is disinfected. Though the boiling point decreases with increasing altitude, it is not enough to affect the disinfecting process.