Hi Amy; I recently visited Ireland in search of my Burke connections, and found dozens in Galway and Mayo counties. They have spread into other counties, and in fact all over the world!
What I did find was that we are all descended from one man, whose name was William De Burgo. He was sent to Ireland by his uncle, Henry II, King of England, as they had all come over from Normandy with William the Conqueror, whose half brother was DeBurgo (same mother, different fathers).
William did so well as a general in the army for his uncle, that he was given vast tracts of land in what is now known as Connaught (which included Galway and Mayo) and married the daughter of the chief King of Ireland, O'Brien. Their son, Richard, became even more powerful and succesful; At one point, after a marraige into the Laceyfamily, they also had control of Ulster, and other parts of Ireland. Some generations later, they changed the family name to Burke, but some branches still call themselves DeBurgo, or DeBourg.
My sister and I have the entire pedigree of this illustrious family from 802 a.d to the mid 1700s, when branches started breaking off and leaving Ireland for the colonies (which included Canada, USA, and the West Indies). After that, it has been hard for us to keep track of where the Burkes have all gone!!