Running injuries are very common, and runners have many different opinions about what causes them and how to prevent them. What is the actual scientific evidence?
Factors you can't easily control
Some factors that you can't easily control play a clear role. These include genetics, being overweight,[Theisen] or having a previous injury. For example, people who want to lose weight may run in order to burn calories; they can't necessarily lose the weight before they start running so as to reduce their chance of getting hurt.
Changes in what you do
There is a large amount of consistent evidence that people get injured more frequently when they make a change in their activity. This could mean changing from stretching to not stretching, changing from not stretching to stretching, wearing different shoes, or running at a different pace or for a different distance.[Pereles,Reynolds]
Stretching and warming up
In general, scientific evidence doesn't support the common belief that stretching before playing sports prevents injuries.[McHugh] Of course this depends somewhat on the sport. In the case of running, a pre-run stretch has been found in a randomized trial to have no statistically significant effect on the incidence of injuries.[Pereles]
Cushioning of shoes
A number of studies have attempted to test whether shoes with more cushioning prevent injury. The results have not always been consistent, but in general there is no clear evidence that cushioning prevents injury.[Theisen] Barefoot runners and runners who use minimalist shoes do not have higher rates of injury, but switching from one type of shoe to another may cause problems; as with any change in what you do, it increases your risk of injury.
Running shoe companies have been telling runners for a long time that they need different shoes depending on whether their feet are normal, pronated, or supinated. This is not true.[Nielsen2]
Repetitive stress injuries
Most running injuries are repetitive stress injuries, or RSI's. As you run, you may be doing tiny amounts of invisible damage to various parts of your body. Normally this damage just heals up and you never even feel it. But if the long-term rate at which you do the damage to a certain body part outpaces the rate at which your body can heal it, your condition will gradually get worse.
As suggested by the term, RSI's are thought to be caused by a stress or load, such as tension or compression, placed on your musculoskeletal system. Most materials behave elastically when subjected to a certain amount of stress, so that when the stress is released, then go back to their original shape. Think of a rubber band being placed under tension, which is then released. But there is a limit on the amount of stress, called the elastic limit. Beyond this limit, the rubber band may be damaged.
When it comes to RSI's caused by running, there has been a lot of speculation that the really damaging stresses are the ones from impacts, such as the heel strike seen in the style of running used by most people who grow up in the industrialized world wearing shoes. The evidence seems to show that what's correlated the most with injuries is not the amount of force (load) experienced by your body parts but the rate of change of the force, which is called the load rate or impact loading.[Zadpoor][Davis] For example, if three people are piled on top of you, lying quietly, then your body is feeling a force equal to four times the usual force of gravity, but the force is not changing, so the load rate is zero. Measurements seem to show that when people wear running shoes, the load rate from their heel strikes is higher than the load rate experienced by barefoot runners.[Lieberman]
Unlike load rate, load itself doesn't seem to be correlated with injury.[Davis] In fact, impact is good for you. Your body seems to need some good hard impacts (about 4 gees or more) in order to have healthy bone density.[Tobias] This is an example of what's known as the "training effect," which is that when you do an activity that results in a certain optimal load, your body gets stronger. However, there is a higher level of load, called the "abusive load," that causes injury.
So the evidence seems to be that you should subject your body to impacts that are of just the right strength, and that they should be applied with a low load rate.
Volume and pace
This makes it pretty complicated to interpret medical studies of running injuries, because usually there is no detailed information about the load and load rate. One hypothesis[Nielsen] is that there are four different variables that should be studied:
There is not much evidence that volume causes injury. For example, one study found that ultramarathoners who ran 200 miles experienced less harm to their bodies than those who ran "only" 100 miles.[Saugy] The interpretation is that at longer distances, runners reduce their pace, reducing the damage to their bodies.
Pace affects load, but it affects load rate even more. Load is proportional to the square of speed, but load rate goes like speed to the third power. For example, if you double your pace, the load rate is eight times higher.
In general, injuries are more likely when you change what you do, and that's the reason for hypothesizing that rapid changes in volume or pace are important variables. However, a study seems to show that the traditional 10% rule, i.e., not to change your volume by more than 10% per week, does not actually reduce injury.[Buist]
In summary, there is not much helpful evidence-based medicine on running injuries. Very little of the conventional wisdom among runners holds up scientifically, so at least you can stop putting time, energy, and money into following their advice. As far as I can tell, the only generic advice that seems to be supported by the evidence is:
Buist, "No Effect of a Graded Training Program on the Number of Running-Related Injuries in Novice Runners: A Randomized Controlled Trial," http://ajs.sagepub.com/content/36/1/33
Kong, "Running in new and worn shoes: a comparison of three types of cushioning footwear," http://www.ncbi.nlm.nih.gov/pubmed/18801775
McHugh, "To stretch or not to stretch: the role of stretching in injury prevention and performance," http://www.ncbi.nlm.nih.gov/pubmed/20030776
Nielsen, "Classifying running‐related injuries based upon etiology, with emphasis on volume and pace," http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3625796/
Nielsen2, "Foot pronation is not associated with increased injury risk in novice runners wearing a neutral shoe: a 1-year prospective cohort study," http://bjsm.bmj.com/content/early/2013/06/12/bjsports-2013-092202.abstract
Pereles, "A Large, Randomized, Prospective Study of the Impact of a Pre-Run Stretch on the Risk of Injury in Teenage and Older Runners," http://www.usatf.org/stretchStudy/index.asp
Reynolds, "Phys Ed: Does Stretching Before Running Prevent Injuries?," http://well.blogs.nytimes.com/2010/09/01/phys-ed-does-stretching-before-running-prevent-injuries/?_php=true&_type=blogs&_r=0
Saugy et al., "Alterations of Neuromuscular Function after the World's Most Challenging Mountain Ultra-Marathon," http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0065596
Theisen, "Influence of midsole hardness of standard cushioned shoes on running-related injury risk," http://bjsm.bmj.com/content/early/2013/09/16/bjsports-2013-092613.abstract
Tobias, "Physical activity and bone: may the force be with you," http://journal.frontiersin.org/article/10.3389/fendo.2014.00020/abstract