One of the most well known and widely used essential oil is Eucalyptus oil. The commonly used one is households is Eucalyptus radiata.
Many of its health benefits includes;
Great remedy for cold and flu (either used for inhalation or put in diffuser or used in the bath)
It is amazing for respiratory problems and can clean wounds due to its antiseptic properties.
"The composition of this oil is such that could be considered an aromatherapist's "designer oil". Together with its attractive fragrance and low price this is the number one all-purpose eucalyptus oil. The combination of terpene alcohols and console is highly effective in treating coughing, sniffles, and a hoarse, scratchy throat. it also contains 3 to 4 percent aldehydes (including neural and geraniol), which lend this oil an especially board spectrum of action (antiviral, expectorant, anti-inflammatory), as well as its exceptionally pleasant aroma."
Source: Kurt Schnaubelt, Ph. D.: Advanced Aromatherapy
Jennie Harding: Secrets of Aromatherapy