SIDS is rare and probably has nothing to do with a baby's position.There's a bunch of research on the subject, and the resulting recommendation is that sleeping on the back is preferred. I haven't read the actual studies, but a bunch are mentioned in the article I linked to:
Alm B, Lagercrantz H, Wennergren G. Stop SIDS - sleeping solitary supine, sucking soother, stopping smoking substitutes. Acta Paediatr. 2006 Mar;95(3):260-2.
Swedish Medical Research Council State of the Art Conference on the Sudden Infant Death Syndrome. Proceedings. Gothenburg, 3-5 June 1992. Acta Paediatr Suppl 1993;389(1):1-129.
Alm B, Milerad J, Wennergren G, Skjaerven R, Øyen N, Norvenius G, et al. A case-control study of smoking and sudden infant death syndrome in the Scandinavian countries, 1992 to 1995. The Nordic Epidemiological SIDS Study. Arch Dis Child 1998;78(4):329-34.
Alm B, Norvenius SG, Wennergren G, Skjaerven R, Oyen N, Milerad J, et al. Changes in the epidemiology of sudden infant death syndrome in Sweden 1973-1996. Arch Dis Child 2001;84(1):24-30.
Alm B, Möllborg P, Erdes L, Pettersson R, Aberg N, Norvenius G, Wennergren G. SIDS risk factors and factors associated with prone sleeping in Sweden. Arch Dis Child. 2006;91:915-9.
Wennergren G. Prevention of sudden infant death syndrome. Pediatr Pulmonol 2004;37 Suppl 26:110-1.
Carpenter RG, Irgens LM, Blair PS, England PD, Fleming P, Huber J, et al. Sudden unexplained infant death in 20 regions in Europe: case control study. Lancet 2004;363(9404):185-91.
American Academy of Pediatrics, Task Force on Sudden Infant Death Syndrome. Policy Statement. The changing concept of sudden infant death syndrome: diagnostic coding shifts, controversies regarding the sleeping environment, and new variables to consider in reducing risk. Pediatrics 2005;116:1245-55.
[edit: google the names of the studies and you'll find abstracts or more]