The question doesn't state what geographical area it's about, and it really isn't possible to give an answer that covers everything. In this answer, I'm only going to deal with pristine backcountry areas in North America, such as the Sierra.
In order to interpret the scientific evidence properly, it's necessary to understand some scientific background about Giardia and giardiasis.
The human gut is naturally teeming with microorganisms. These are known as your gut flora or gut microbiome. Most of these are bacteria, but quite a few are other organisms, including protozoans such as Giardia. Some of these critters in your intestines are beneficial or even necessary for your metabolism, while others may be neutral or harmful. People tend to develop tolerance for their own gut flora, but can get sick from other people's. The gut microbiome tends to be more diverse among people in the developing world, less so in the developed world, and this decreased diversity may actually be a bad thing.
Giardia is present in about 3-7% of adults in the US, about 30% in the developing world.[Auerbach 2012] Among toddlers in the US, roughly a third have it.[Ish-Horowicz 1989] Most people who have Giardia as part of their gut flora have no symptoms at all, which is why you don't see a third of toddlers with miserable cases of diarrhea at any given time. Among people who do have symptoms, the condition is normally mild and self-limiting. For unknown reasons, there is a small portion of the population that tolerates Giardia badly if newly introduced to it, and these people have unpleasant diarrhea for some period of time.
Giardia is present in surface water in the form of dormant cysts. These cysts tend to resist being killed by chlorine. You can pick up Giardia by drinking water that contains cysts, but what was not realized in the 1970s, during the initial Giardia public-health panic, was that Giardia is also transmissible through hand-to-mouth contamination. In the context of backpacking, this would something like the following. A and B go backpacking together. A has Giardia in her gut microbiome, and she tolerates it and has never had any symptoms. B doesn't have it. A poops and doesn't wash her hands, and then A and B have dinner together and share pots and pans. B eats food that is contaminated with A's Giardia.
Many people use Giardia as a sort of generic term, like "xerox" or "kleenex." For this reason, it is common to hear backpackers claim that they "got Giardia," when all they really know is that they got sick. They could have had some other condition, they could have had giardiasis but contracted it somewhere else, or they could have gotten a bug through hand-to-mouth contamination from their hiking partners.
Often people will make this claim when they got sick during the hike. This is unlikely. When an animal is infected by a parasite, there's a prepatent period, which is the time from infection with a parasite to when the bugs reach a life stage where they can be detected by a lab test. There's also an incubation period, which is the time from infection to symptoms. For most parasites, the prepatent period is shorter than the incubation period, but for Giardia it's often longer. A 1954 study on prison volunteers showed an average prepatent period of 9 days, but there's a wide range of variation, and the incubation period can be as long as months. In a study of travelers to the Soviet Union, the typical time until acute symptoms occurred was found to be a couple of weeks. In about two thirds of patients, the prepatency period was longer than the incubation period by a week or more. In summary, if someone gets backpacker's diarrhea while on a weekend backpacking trip, it's very unlikely that it was caused by giardiasis that they acquired during the trip.
As stated above, my answer only deals with pristine backcountry areas in North America. Some studies have surveyed water in these areas for Giardia.[Suk 1986],[Jaret 2003] The water was extremely clean, and huge volumes of it had to be filtered in order to pick up any detectable number of Giardia cysts. For example, there were sites in the Sierra where they filtered 100 gallons of water and didn't detect a single Giardia cyst left over in the filter. In most of the locations where cysts were detected, the concentrations were so low that they have to be expressed in scientific notation. In low-use areas, they ranged from zero to about 5x10^-3 per liter, while one high-use area had about 0.1 per liter. Elsewhere in the U.S., similar testing also found extremely low concentrations all of the backcountry locations tested: West Beaver Creek, AZ; Merced River, CA; Chattooga River, NC;
Neversink River, NY; White Pine Lake, UT; Greenwater River, WA; and Renard Lake, WI.
From these studies, it appears that if you spend a weekend drinking untreated water in pristine backcountry areas in the US, you will typically not ingest a single Giardia cyst. We then need to do a risk-benefit analysis. This raises the question of how many cysts you need to swallow in order to have a certain chance of getting infected, as well as the chance that this will cause symptoms. The best single source of information on the first question is a 1954 study by Rendtorff that used prison volunteers; the data are summarized and analyzed further by [Cox 2002] and [Rose 1991]. Roughly speaking, you have to ingest about 20-30 cysts to be likely to get an infection.
It would be interesting to know whether there is a threshold effect, i.e., whether or not there is some chance, however small, of getting sick by swallowing a single cyst. The data are not sufficient to determine this. Rose introduces a mathematical model in which it is assumed that each cyst has some probability p of setting up shop in your gut, but this is an assumption of the model, and is not testable based on the data, which used higher doses. Rose's model is also not consistent with data showing that even when people drink very highly contaminated water, there is still only about a 50% chance of contracting giardiasis.[Wilkerson 1992] In this type of study, one of the confounding factors is that the minimum infectious dose can vary depending on the strain of the microorganism.
If you do pick up a giardia infection, and if you weren't already an asymptomatic carrier, then it appears that your chance of developing symptoms is about one in 10.[Wilkerson 1992]
Based on these numbers, we can make at least a rough order-of-magnitude estimate of the risk associated with drinking backcountry water. Suppose you go on a weekend hiking trip in the Sierra and drink 6 liters of untreated water. In low-use areas, the concentration of Giardia cysts in your water appears to average about 3x10^-3 per liter. Based on Rose's model, take the probability of infection to be about p=.02 per cyst. If infection occurs, the chance of getting symptoms (which are in most cases mild) is on the order of 0.1. Multiplying these factors, we arrive at a probability of about 4x10^-5 that you will get Giardia symptoms. That is, under these assumptions, out of a million people who do this, about 40 are expected to get diarrhea.
This estimate appears to conflict with a study by Zell,[Zell 1993] which states:
The incidence of Giardia cyst acquisition in backcountry travelers was
only 5.7% (95% CI 0.17–20.2%). Mild, self-limiting gastrointestinal
illness occurred in 16.7% of subjects (95% CI 4.9%–34.50%), none of
whom demonstrated G. lamblia infection.
Although none of the people in the study who had Giardia got symptoms, this rate of infection is many orders of magnitude higher than would have been expected from water contamination based on the Rendroff-Rose data and modeling. Unfortunately the Zell article is paywalled, so I can only see the abstract, but it appears that he would have had no way to tell whether the people who acquired infections got them from contaminated water or from hand-to-mouth contamination. In any case, Zell's conclusion is that water treatment is of marginal cost-effectiveness, given the low risk and the fact that the infection is self-limiting and usually asymptomatic.
Another reality check we can do is to compare the concentrations of Giardia in backcountry water with the concentrations in city tap water. This is complicated by the fact that Giardia cysts, whether found in backcountry water or tap water, may be nonviable, and surveys cannot usually determine their viability. Historically, city tap water has been getting cleaner and cleaner, especially in the developed world. However, it appears to have been normal in 20th-century America for city tap water to contain concentrations of Giardia cysts that are similar to or greater than the concentrations found in backcountry areas of the US.[Rockwell 2002] It would be interesting to get more detailed information on this from someone who has professional-level knowledge of US water supplies and their history.
A meta-analysis of the literature in 2000 concluded that "the evidence for an association between drinking backcountry water and acquiring giardiasis is minimal."[Welch 2000] When people do actually contract backpacker's diarrhea from exposure during a hiking trip, by far the most common reason is hand-to-mouth contamination.[Welch 1995]
Auerbach 2012 - Paul S. Auerbach, Wilderness Medicine (6th ed., 2012), ch. 68
Cox 2002 - Cox, F.E.G. (2002). History of Human Parasitology. Clin. Microbiol. Rev. 15(4): 595
Erlandsen 1984 - Erlandsen, Giardia and giardiasis: biology, pathogenesis, and epidemiology, 1984.
Ish-Horowicz 1989 - Ish-Horowicz et al., "Asymptomatic giardiasis in children," Pediatr Infect Dis J. 1989 Nov;8(11):773-9.
Jaret 2003 - Peter Jaret, "What's In the Water?," Backpacker, Dec. 2003, p. 45.
Jokipii, The Lancet, Volume 309:1095.
Rockwell 2002 - Robert L. Rockwell, Sierra Nature Notes, Volume 2, January 2002, http://web.archive.org/web/20051026030831/www.yosemite.org/naturenotes/Giardia.htm
Rose 1991 - Rose, Haas, and Regli, "Risk assessment and control of waterborne Giardiasis," Am J Public Health 81 (1991) 709, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1405147/pdf/amjph00206-0039.pdf
Suk 1986 - Map cited as reference 17 in S.C. Zell, "Epidemiology of wilderness-acquired diarrhea: implications for prevention and treatment," Wilderness and Environmental Medicine 3 (1992) 241, http://www.wemjournal.org/article/S0953-9859(92)71235-2/abstract
Welch 1995 - Thomas R. Welch and Timothy P. Welch, "Giardiasis as a threat to backpackers in the United States: a survey of state health departments," Wilderness and Environmental Medicine, 6 (1995) 162, http://www.wemjournal.org/article/S1080-6032%2895%2971046-8/abstract
Welch 2000 - Welch, T.P. "Risk of giardiasis from consumption of wilderness water in North America: a systematic review of epidemiologic data," Int J Infect Dis. 2000;4:103100, http://download.journals.elsevierhealth.com/pdfs/journals/1201-9712/PIIS1201971200901024.pdf?refuid=S1080-6032(04)70498-6&refissn=1080-6032&mis=.pdf
Wilkerson 1992 - Wilkerson, James A., MD: Medicine for Mountaineering and Other Wilderness Activities. The Mountaineers, 4th edition, 1992 (referenced in Rockwell, http://web.archive.org/web/20051026030831/www.yosemite.org/naturenotes/Giardia.htm )
Zell 1993 - Zell and Sorenson, "Cyst acquisition rate for Giardia lamblia in backcountry travelers to Desolation Wilderness, Lake Tahoe," Journal of Wilderness Medicine 4 (1993) 147.