dangers
bacteria (e. coli, salmonella, listeria, shingella, campylobacter)
Chemical treatment, filtration, and pasteurization are all able to remove bacteria (at differing levels of ease).
e. coli
The most prevalent bacterial contaminant in backpacking. Which can give you hemorrhagic colitis which in very serious circumstances can actually lead to kidney failure.
Most bacteria are harmless, a subset of those called "fecal coliforms" are also mostly harmless, but contain E. coli. Even E. coli itself is usually harmless, but a few rare strains (such as O157:H7) can cause serious ilness. Unfortunately most water safety reports don't report "dangerous strains of E. coli" but rather simply report "total coliforms". The minimum effective dose seems to be 5-10 cells, but it's a bit hard to know for sure since the counting methods are somewhat flawed.
Dog droppings are generally the leading cause of E. coli, especially in the outdoors. A single gram averages 20,000,000 E. coli colonies. In practice, there was a study throughout the desolation wilderness where many sites had none, some had 100-300 cells per liter, and notably a spigot near a ranger station had 2000 cells per liter.
All EPA certified filters will have at least 6 log reduction meaning drinking
from that spigot will have 0.002 cells per liter or a 1 in 2500 chance of the
minimum 5 cells from a fairly bad source. However, at such faucets you'll be
filling multiple liters normally. It gets worse though, these "cells" in this
context are generally observed clusters of cells which could be around a dozen
actual cells basically taking our odds down by a factor of 10, meaning 1/250 per
liter which is pretty bad when drinking multiple liters on a long trip
especially for getting a potentially fatal disease. You might realistically want
7 or 8 logs in most situations, which is available from several filters
including the sawyer mini.
viruses (norovirus, hepatitis a.)
Normal backpacking microfilters are unable to remove most common viruses. Chemical treatment however will easily kill viruses. Most backpacking water sources in the US are fairly safe from viruses, but in some other places it can be an issue.
It turns out there's a very widespread myth regarding the size of a virus being
at it's minimum 0.004 microns. It seems as if the myth originates from a
subtle mistake/typo/etc made in the book "Medicine for Mountaineering & Other
Wilderness Activities" in chapter 5.
So what size is the "minimum" for a virus? Well, turns out we don't know for
certain, but there are many reputable manufacturers producing independent lab
results (including military) which show several log reduction for viruses with
filters of only 0.02 microns. The CDC also officially states that 0.01
micron filters should be effective at removing viruses, bacteria, and parasites.
They also state that the average virus size is 0.03.
cysts (giardia, cryptosporidium)
While easily killed with pasteurization or filtration, they can prove difficult and time consuming for chemical treatments.
giardia
Giardia is one of the most common diseases worldwide that is carried by water. Generally speaking this is what you're most likely to contract on the trail. Like many other contaminants it is found in poop. A single gram can contain a million cysts. (With the average minimum effective dose being just 10 cysts).
When infected you will not always develop symptoms and if you do catch it the incubation period lasts 1-2 weeks with a mean of 9 days, so the water source in question if often misattributed.
Symptoms might include watery diarrhoea alternating with greasy stools. Fatigue, cramps and belching wind may also occur. Some people have no symptoms. Most cases clear up on their own within a few weeks. Severe cases are treated with antibiotics.
cryptosporidium
The most chemically resistant of the common cysts. Chlorine dioxide is the only chemical able to treat it and even then it takes 4 hours for an acceptable level. It's often best to use a combination of chemical and microfiltration or pasteurization if you're drinking from a source with dead animals or waste.
It can cause a respiratory and gastrointestinal illness that primarily involves watery diarrhea sometimes with a persistent cough. Treatment of gastrointestinal infection in humans involves fluid rehydration, electrolyte replacement, and management of any pain. Supplemental zinc may improve symptoms.
Unlike giardia, the minimum effective dose is just a single cyst. So although it's less prevalent in water sources and is often in lower quantities, it's significantly easier to catch.