Q:

Do running shoes prevent injury?

One common question among runners is when to replace your shoes, with the popular advice ranging anywhere from 300 to 600 miles (482 to 966 kilometers). The justification for doing so is not that the shoe are worn through, but rather:

Don't use the treads of your running shoes to determine whether you
  should replace your shoes. The midsole, which provides the cushioning
  and stability, usually breaks down before the bottom shows major signs
  of wear. If you've been feeling muscle fatigue, shin splints, or some
  pain in your joints -- especially your knees -- you may be wearing
  running shoes that no longer have adequate cushioning.

Which means that a lot of runners will replace shoes that look to be in fairly good condition in hopes of avoiding injuries. 
However, one of the many claims that the book "Born to Run" by Christopher McDougall makes is that there is no evidence that running shoes prevent injury. Specifically the book says the following,

In a 2008 research paper for the British Journal of Sports Medicine,
  Dr. Craig Richards, a researcher at the University of Newcastle in
  Austria, revealed that there are no evidence-based studies - not one
  - that demonstrate that running shoes make you less prone to injury.

Where injury is generally defined as conditions such as Plantar Fasciitis as opposed to minor cuts and scrapes to the foot due to the running surface or hazards on it.
Is this claim accurate? Is there no evidence that running shoes prevent injury?

A:

The contrary is in part true, in that running barefoot rather than wearing shoes with thick padding and cushioning tends to decrease injury and strengthen the foot and leg muscles.
http://en.wikipedia.org/wiki/Barefoot_running 

The running shoe itself has also been examined as a possible cause of many injuries associated with shod running. One 1991 study found that wearers of expensive running shoes that are promoted as having special features, such as added cushioning or pronation correction, were injured significantly more frequently than runners wearing inexpensive shoes.[10] It has also been found that running in conventional running shoes increases stress on the knee joints up to 38%, although it is still unclear if this leads to a higher rate of heel injuries or not.[32][33][34] One study suggests that there is no evidence that cushioning or pronation control in shoes reduces injury rates or reduces performance.[35] It was also found that the belief that one's shoes have increased cushioning had no effect on increasing or decreasing ground reaction forces during walking.[36] Modern running shoes can also increase joint torque at the hip, knee, and ankle, and the authors of the study even suggest that running in high heels might be better than modern running shoes.[37] Improperly fitting shoes may also result in injuries such as a subungual hematoma – a collection of blood underneath the toenail. This may also be known as "runner's toe" or "tennis toe".[38]

(references in the original).
http://www.sportsci.org/jour/0103/mw.htm says basically the same:

Running barefoot is associated with a substantially lower prevalence of acute injuries of the ankle and chronic injuries of the lower leg in developing countries, but well-designed studies of the effects of barefoot and shod running on injury are lacking. Laboratory studies show that the energy cost of running is reduced by about 4% when the feet are not shod. In spite of these apparent benefits, barefoot running is rare in competition, and there are no published controlled trials of the effects of running barefoot on simulated or real competitive performance.

And again here http://www.sciencedaily.com/releases/2010/01/100127134241.htm

That said, it seems logical to assume that having a worn out shoe with damaged support structures and sole will yield to a higher chance of injury than a fresh one (IF they were properly fitted in the first place of course). 

