The secular games, ludi saeculares, were spread over a period of three days and in theory they were supposed to have been celebrated once in a lifetime, which was fixed at a maximum of 100 or 110 years. They seem to have been instituted under Augustus, but attempts were made to link them with games variously called ludi tarentini, ludi terentini, or ludi taurii, founded in the time of the kings or the early Republic.
As the historical details of the earlier celebrations were vague even to the Romans, if an emperor wanted to celebrate them a formula could be found to get them to fall on the right date. We know of celebrations under Augustus (17 BC), Claudius (47 AD – the 800th anniversary of the founding of Rome), Domitian (88 AD), Antoninus Pius (147 AD – the 900th anniversary of the founding of Rome),Septimius Severus (204 AD), and Philip the Arab (248 AD – the 1000th anniversary of the founding of Rome), though there is some confusion about whether the celebrations by Claudius (see this thread from Classics-L: Claudius and the ludi Saeculares), Antoninus Pius, and Philip the Arab, really counted as ludi saeculares or not.
Zosimus describes what went on at the secular games and their alleged origin and history.
Apparently, it is now Poetry Month in the USA, and in honour of the occasion, the Ancient/Classical History section of About.com has a special feature on Horace, including another translation of the carmen saeculare (scroll about three quarters of the way down the page).
Postscript from Irene: For those who have JSTOR access,
there is an article by Lily Ross Taylor:
New Light on the History of the Secular Games, The American Journal of Philology, Vol. 55, No. 2. (1934), pp. 101-120.