Yes, dogs can be trained to alert to scents, such as the scent in the perspiration of a person with low blood sugar due to diabetes. Other animals can be trained as well. In Africa, rats are trained to detect tuberculosis: http://www.apopo.org/cms.php?cmsid=107
Trained response dogs are probably more reliable though, as well as easier to train. For example, there are seizure response dogs and seizure alert dogs. Seizure response dogs are trained how to respond to a seizure, whereas alert dogs are trained to alert a person to an oncoming seizure.