O’Connor was one of the most popular names in old Ireland, and at least six distinct septs arose in different parts of the country. The Connacht O’Connors included O'Connor Don, O’Connor Roe and O’Connor Sligo. Clonalis House in County Roscommon is the ancestral seat of the Connacht O'Connors, whose ancestry included 11 High Kings and 24 Kings of Connacht. Ballintober Castle, near Castlerea, was the stronghold of the O'Connors of Connacht from the early 14th to the 17th centuries.
The first O’Connor High King was Connor MacNessa. He is often described as the greatest of all the O’Connor kings. He reigned during the quest for Cooley’s Bull, and married Maedb, warrior queen of Connacht. After they separated, he married her sister, Ethne. Connor was a patron of the arts and learning of all kinds, and he was the first to open the hereditary professions to all comers.
The last two High Kings of Ireland were Turlough (Toirdelbach) O’Connor, who died in 1156 AD, and his son Roderick (Ruadri) O’Connor, who died in 1198 AD. His brother, Cathal Crovderg (died 1224 AD) was a King of Connacht. The title of O’Connor Don has been passed down to each new chief of the Connacht O’Connors, representing their right to the kingship of Ireland. In 1912, Sir Bernard Burke, Ulster King of Arms, said of the O’Connor Don: “No family in Ireland claims greater antiquity and no family in Europe, royal or noble, can trace its descent through so many generations of legitimate ancestors.” The present O’Connor Don is Denis O’Conor. It is generally believed in Ireland today that if there were to be a new King of Ireland, Denis O’Conor would have first claim to the title.
When Peter O’Connor of Thurles, Ireland, won a gold medal in the 1906 Olympics, he climbed the flagpole at the presentation of his medal to replace the Union Jack with the flag of Ireland.
Achievements of O’Connor’s in the US include attorney Charles O’Connor (1804-1884), who was the first Catholic ever nominated for the office of President of the United States, when the “Straight out Democrats” refused to accept the candidacy of Horace Greeley (O’Connor refused to run). Colonel Brian O’Connor (USMC) is a NASA astronaut who has logged over 383 hours in space, piloting the crew of a mission in 1985 and commanding the crew of a mission in 1991. Sandra Day O'Connor is one of the nine Supreme Court Justices.
***Disclaimer -- The following is a collection of information from several O'Connor websites, but some Irish history buffs disagree with some of it, including (1) the statement that the name O'Connor descends from the Middle English, (2) that Conchobar Mac Neasa was an O'Connor, (3) that there were more than two High Kings who were O'Connors, and (4) that any information dating from before the introduction of writing in Ireland in the 5th Century can be relied on as being true. I note these dissenting opinions here; however, I believe that the historical information I have found supports the information below.
The name O'Connor comes from Middle English connere, cunnere = inspector, from cunnen =
to examine, from Old English cunnan = to know. It was the occupation of the man who inspected for standards, including weights and measures. The Clan O’Connor (Gaelic O'Conchobhair) in Connacht descends from Conchobhar, whose name means ‘lover of wolves.’ Conchobhar descended from Brion, the first son of Eochaidh Muigh-Meadhoine, the 124th monarch of Ireland. Eochaidh ruled as King of Connacht from 358 AD to his death in 366 AD. Brion founded the Ui Briuin, from whom descended the Ui Briuin Ai (O’Connors). Conchobhar, son of Donnchadh, was a King of Connacht who died in 970 AD. He adopted the hero Cuchulain. 
The O'Connor Dress Tartan