We all know that dogs have an amazing sense of smell, and we have utilized this fact for many years in tracking and drug detection. Dogs smell in parts per trillion, to illustrate this to you, if you put a drop of blood in 3 Olympic-sized swimming pools; a dog would smell this blood.
Recent studies have shown that dogs can be trained to sniff out cancers of the lung, breast, skin, bladder and prostate. In a 2011 study, lung cancer was identified with a sensitivity of 71% and a specificity of 93%.In another study 66 patients referred to a urologist were selected, 33 confirmed with prostatic cancer and 33 controls. Belgian Malinois Shepherd Dogs picked 30 of the 33 positives correctly. 
Other amazing medical applications of dogs’ sense of smell include their increasing use as service animals for people with diabetes, where they can detect fluctuations in blood sugar (dangerous for diabetic patients) and alert them even before they feel symptoms.
Apparently dogs have also been documented to detect epileptic seizures 45 minutes before they occur. Scientists still have no idea how this occurs.
1. Ehmann R, Boedeker E, Friedrich U, et al. (August 2011). “Canine scent detection in the diagnosis of lung cancer: Revisiting a puzzling phenomenon”. Eur Respir J 39 (3): 669–76. doi:10.1183/09031936.00051711. PMID 21852337.
2. Cornu JN, Cancel-Tassin G, Ondet V, Giardet C, Cussenot O (2010). Olfactory detection of prostate cancer by dogs sniffing urine: a step forward in early diagnosis. Eur Urol. 2011 Feb;59(2):197-201. doi: 10.1016/j.eururo.2010