Bro. Glen, there are two generally recognized events called the Great Awakening.
The first occurred in the mid-17th Century and is exemplified by Jonathan Edwards in the United States, the Wesleys in Britain and George Whitefield in both. Whitefield is an interesting connection between the two.
The first was marked by emotionalism, conversions and itinerant preachers who preached to large crowds outside of churches. (Whitefield is said to have preached to 20,000 people in Boston at a time the entire population of the city was only slightly larger than that.) The Baptists, Presbyterians and Methodists, in particular, grew as a result.
The Second Great Awakening began in the early 1800s in the United States and was characterized not only by revivalism but also by the development of new sects and denominations -- Mormons, Adventists, Campbellites, Disciples of Christ, etc. It also promoted the creation and development of mission societies, both within and among denominations.
A case could be made that there have been others that deserve the title, such as the development of Pentecostalism in the early 1900s and what is happening today, which has been called the "Third Wave."