Does culling badgers restrict the spread of bovine tuberculosis?
This is apparently a debate since decades in the UK. As to the pathology:


  Eurasian badgers (Meles meles) are an important wildlife reservoir of
  tuberculosis (Mycobacterium bovis) infection in Ireland and the United
  Kingdom. As part of national programmes to control tuberculosis in
  livestock, considerable effort has been devoted to studying the
  disease in badgers and this has lead to a rapid increase in our
  knowledge of tuberculosis in this host.


L. A. Corner, D. Murphy, E. Gormley: Mycobacterium bovis infection in the Eurasian badger (Meles meles): the disease, pathogenesis, epidemiology and control.'' In: ''Journal of comparative pathology. 144, 1, January 2011, 1–24. doi:10.1016/j.jcpa.2010.10.003. PMID 21131004. (Review).

A summary of the pre-1997 debates is here:
http://archive.defra.gov.uk/foodfarm/farmanimal/diseases/atoz/tb/publications/krebs.htm

The up-to-date DEFRA informations are at:
http://www.defra.gov.uk/animal-diseases/a-z/bovine-tb/

For an alternative approach see:
http://www.ncbi.nlm.nih.gov/pubmed/19846226 (in short: educate them not to piss everywhere)

I have been asked to give also a summary. Tuberculosis is probably one of the nastiest bacterial infections in existence. It is a prototype of those diseases which are called latent: you can be infected for decades without symptoms, but when your immune system falters (or you have to take immune suppressants) it breaks out and kills you. One third of the human population has such a latent infection with Mycobacterium tuberculosis, and the HIV wave plus the high mycobacterial mutation rate with following extreme resistances make for interesting epidemiology. But this is also a result of our lifestyle, depending on huge cattle herds, as cattle can be cross-infected with human TB. In the west we have succeded to cut human infections by controlling cattle infection with human TB. Still, cattle can get bovine TB, and this may be economically disastrous. One of the pools of the infection is the badger population which can get bovine TB too and spread bacteria with their urine. It is unclear if protozoa may be an even more important pool. It is likewise unclear if culling of badgers would be successful for cattle TB control; the government bases its decision on a long-term study of regions where culling has happened. Alternative approaches include vaccination (which only affects uninfected animals), different cattle grazing regimes, habitat manipulations and badger latrine management. Physical exclusion of badgers from farm buildings is suggested as the simplest, and potentially most effective, method of reducing contact and opportunities for disease transmission between badgers and cattle. The government expert opinion clearly concluded that without such additional measures, culling won't be successful in reducing cattle TB.