Although Savory is largely a culinary herb, it contains oils and tannins that have mild astringent and antiseptic properties that can be useful in medicines.  Summer Savory (pictured here) is the type most often used for medicinal purposes.  Teas can be made for occasional colic, diarrhea, indigestion, flatulence, stomach upsets, mild sore throats, and as an expectorant.  It is also sometimes used in a tea by diabetics to alleviate excessive thirst.  Capsules can also be made from dried leaves for internal use. 

Externally, rubbing a sprig of Savory on wasp or bee stings provides instant relief.  Try using an Ointment made of Savory for minor rashes and skin irritations. 

Historically, Savory has a reputation for regulating sex drive.  Winter Savory is said to decrease sex drive, while Summer Savory is said to enhance it.  (I vote for Summer Savory :)