For every "I drink from running water and have never been sick" story, there are a hundred
of these . You can hike upstream all you like, but unless you hike to the source there is always a chance something unpleasant is festering just a bit further along, or somebody/something else who is infected with something decides to take a swim (and take a pee, why not?) or wash dishes or whatever at the next campsite up. Having said that, I spent my early years without treating the water I drank, and my parents and their friends still don't treat their water. They are old-school campers, to say the least.
We do chemical treatment, boiling or filtering depending on the situation. If necessary, we will prefilter with some old pantyhose to take as much detritus out as possible, then move on to another method. I use an MSR MIOX for when we're out in a group; it takes time but it does large volumes with little work. When done right, the chlorine taste evaporates off overnight. Of course, many use pump-action filters for the same job; MSR and Katadyn both make models that are popular out here. They treat small volumes (less than 4 L) very quickly, but require you to pump like mad. Boiling is always on the table, and most of our food is "add boiling water", so it's a no brainer.
We usually go like this: We hit our campsite and start to set up. Once our gear is spread around, tents and tarps are up and beds made, somebody goes to get water, usually in a big collapsible jug. Some of that water is poured off for boiling right away; hot drinks or a meal are usually what is on our minds. Meanwhile, somebody else treats the remaining water in the jug. That is allowed to sit for a while to purify, and gets used for camp chores for the evening. We refill our water bladders so they're ready to go in the morning and try to leave enough water for dishes in the morning.
The next am, somebody goes to the river and gets a big pot of water for breakfast and boils it. Eat, break camp and march on.