Which Prominent Modern Religions Came from the "Great Awakenings" and What Have They Done For the World?

In short, the "mainline" Christian denominations/religions existed before the "Great Awakenings," although smaller denominations/religions such as the LDS, the Seventh Day Adventists, the JW emerged through these periods of revival. The "Evangelical" denominations emerged out of a separate revivalist tradition centered on the West Coast around the turn of the 20th Century (for more info read Hayford, Jack W.; Moore, S. David (2006). The Charismatic Century: The Enduring Impact of the Azusa Street Revival).

A longer answer really begins to question whether the historical theory of the "Great Awakenings" is even correct. Jon Butler most famously attacked the theory of the "First Great Awakening" in his book Awash in a Sea of Faith. Butler argues that the traditional theory of Christian Revival spurring on Revolutionary fervor in the years leading up to the American Revolution is invalid and that there is no evidence for a wide-spread revival like traditional textbooks teach. No other historian has been able to completely refute his claims in these regards. However, there is no way to ignore the major revivals in the 1740s and 50s in New England. These revivals though, led to more schism within the Congregationalist tradition than positive change.

The "Second Great Awakening" is the movement which produced smaller denominations/religions such as the LDS, the Seventh Day Adventists, and the JW. The "Second Great Awakening" occurred in the aftermath of the American Revolution, although it was more of a reaction to the departure of the Church of England and its missionary societies. When Church of England clergy and money left the colonies, there was a void to be filled in American religious life. This second "Awakening" is what made the Mainline denominations mainline. In many colonies they took over former Church of England buildings and congregations. It took many years from the departure of the Church of England for the Mainline denominations to completely organize themselves[edit: in the modern legal sense]; and within this time, doctrine within the Methodist, Presbyterian, and Baptist movements were fairly fluid. In her book Southern Cross, Christine Heyrman writes how a Methodist revivalist could found a Baptist congregation because of doctrinal confusion and petty squabbling amongst congregants. This doctrinal confusion led to the creation of more denominations.

Getting back to your question, the "Great Awakenings" led to the creation of new denominations/religions because of confusion over doctrine and squabbling. I am personally more of a historian than a theologian, so I leave it up to others whether this was an issue of true doctrinal disputes or an issue of schism. This is also a very broad summary of very complex movements, and I am sure I have failed to do them justice in some regards, but this is generally how current research perceives the "Great Awakening"s.

The most significant influence that the "Great Awakenings" have had that is generally upheld by scholars is making religion more individualistic. The theology of Catholics, Lutherans, and Anglicans/Episcopalians is generally collective (e.g. the Church and her sacraments being important in an individual's salvation) while the "revival theology" of most Protestant denominations is much more individual (e.g. the emphasis on personally receiving Christ and even hymns such as "O What a Friend We Have in Jesus"). A lot of this "revival theology" comes out of the "Great Awakenings"

I know this was quite long, but I hope this helps you.