Nick is right, high top shoes (boots) provide very little actual ankle support, though they do provide a feeling of support.
A while ago I did some research of the scientific literature, while some studies suggested that high tops might offer some support the general consensus of the papers that reviewed the literature was that they do not.
This is a link to a very vigorous debate on the topic on another forum. http://tasmania.bushwalk.com/forum/viewtopic.php?f=15&t=3365&hilit=running+shoes
Here is a small selection of conclusions.
Prevention of Acute Ankle Ligament Sprains in Sport
Martin P. Schwellnus
The factor in footwear design that has most frequently investigated is the possible role of high-top shoes in reducing the risk of ankle sprains (Petrov 1988). The results from three studies indicate that, in the absence of additional taping or external support, wearing high-top shoes does not reduce the risk of ankle sprains. Indeed, in one study, the wearing of low-top shoes resulted in a lower incidence of ankle sprains compared to high-top shoes (Rovere et al. 1988). In two recently published meta-analysises, it was also concluded that the role of footwear in the prevention of ankle sprains was not clear (Quinn et al. 2000).
In summery, although a protective influence of footwear is suggested from the results of biomechanical studies, footwear without additional support from taping and bracing does not appear to have a strong influence on the risk of ankle sprain. The potential negative effect that footwear may have on the proprioceptive function of the foot requires further investigation.
Effect of High-top and low-top shoes on Ankle inversion
Mark D. Ricard, PhD; Shane S. Schuties, PhD, PT, ATC; Jose J. Saret, MS, ATC
Conclusions: The high-top shoes were more effective in reducing the amount and the rate of inversion than low top shoes. Depending on the load conditions, high-top shoes may help prevent some ankle sprains.
This is from the introduction
High-top athletic shoes are frequently to augment ankle support because they may provide increased resistance to inversion. The increase cost of these shoes may be justified if they decrease ankle injury rates. Not all studies, however, support the finding that high-top shoes may reduce the potential for injury. Currently, consensus is lacking among researchers and clinicians concerning the extent to which high-top shoes protect the ankle from inversion trauma.
1: Foot Ankle. 1991 Aug;12(1):26-30.
Risk factors for lateral ankle sprain: a prospective study among military recruits.
Milgrom C, Shlamkovitch N, Finestone A, Eldad A, Laor A, Danon YL, Lavie O, Wosk J, Simkin A.
Department of Orthopaedic Surgery, Hadassah Hospital, Ein Kerem, Jerusalem, Israel.
In a prospective study of risk factors for lateral ankle sprain among 390 male Israeli infantry recruits, a 18% incidence of lateral ankle sprains was found in basic training. There was no statistically significant difference in the incidence of lateral ankle sprains between recruits who trained in modified basketball shoes or standard lightweight infantry boots. By multivariate stepwise logistic regression a statistically significant relationship was found between body weight x height (a magnitude which is proportional to the mass moment of inertia of the body around a horizontal axis through the ankle), a previous history of ankle sprain, and the incidence of lateral ankle sprains. Recruits who were taller and heavier and thus had larger mass moments of inertia (P = 0.004), and those with a prior history of ankle sprain (P = 0.01) had higher lateral ankle sprain morbidity in basic training.
1: Sports Med. 1995 Oct;20(4):277-80.Links
The role of shoes in the prevention of ankle sprains.
Barrett J, Bilisko T.
University of Oklahoma, Health Sciences Center, Oklahoma City, USA.
Ankle sprains are a common sports injury that can cause significant, chronic disability. Studies aimed at prevention through the use of footwear have focused on the biomechanical aspects of foot and ankle anatomy, proprioceptive input of the foot/ankle complex, external stresses applied to the joint, and shoe traction. These studies support the use of high top shoes for ankle sprain prevention because of their ability to limit extreme ranges of motion, provide additional proprioceptive input and decrease external joint stress. Despite this biomechanical evidence, clinical trials are inconclusive as to the clinical benefit of high top shoes in the prevention of ankle sprains. Further study is necessary to delineate the benefits of shoe designs for ankle sprain prevention.
Some other information about ankles
If you have already sprained your ankle you are more likely to sprain your ankle again than someone that had not sprained his or her ankle before.
Athletes who have suffered a previous sprain decreased risk of injury if a brace is worn.