Upper-class Romans were typically spectators, not performers, of dance.

At least some elite Romans, in fact, considered participating in a dance nothing less than shameful. Cicero, for example, is at pains to explain why one of his clients - accused of being a dancer - would never stoop or shimmy so low:

"Cato calls Lucius Murena a dancer....you ought not [O, Cato] rashly to call a consul of the Roman people a dancer...For no man, one may almost say, ever dances when sober, unless perhaps he be a madman, nor in solitude, nor in a moderate and sober party; dancing is the last companion of prolonged feasting, of luxurious situation, and of many refinements." (Pro Murena 1.6)

It was perfectly legitimate, however, for elite Romans to dance in certain religious contexts. Only patricians, for example, could be Salii - the dancing priests of Mars. Twice a year (probably), 24 of these men would put on a stylized version of ancient armor and process through the city of Rome, pausing at intervals to perform an elaborate dance while clashing their shields and singing ancient songs. The dance itself (the tripudium) seems, like the Pyrrhic dances of ancient Greece, to have evolved from military exercises. Plutarch gives a disappointingly brief description: "the dance is chiefly a matter of step; for they move gracefully, and execute with vigor and agility certain shifting convolutions, in quick and oft-recurring rhythm" (Numa 13).

Roman women might also dance in ritual contexts. A traditional (and therefore respectable) example was the "rope dance" at least occasionally performed to honor Juno. As described by Livy:

"Then the seven and twenty maidens in long robes marched, singing their hymn in honor of Juno the Queen...From the gate they proceeded along the Vicus Iugarius into the Forum. In the Forum the procession halted, and passing a rope from hand to hand the maidens advanced, accompanying the sound of the voice by beating time with their feet." (27.37.12-14)

Other sacred dances were less reputable. The Galli - the eunuch priests / devotees of the Anatolian goddess Cybele, whose worship had been imported to Rome in the third century BCE - were known for their ecstatic dances, which often seemed disturbingly exotic and indecorous to the Romans. Their fascination and otherness are captured by a passage from Lucretius:

"The Galli come: and hollow cymbals, tight-skinned tambourines resound around to banging of their hands; the fierce horns threaten with a raucous bray; The tubed pipe excites their maddened minds in Phrygian measures; they bear before them knives, wild emblems of their frenzy, which have power to panic with terror of the goddess' might the rabble's ingrate heads and impious hearts" (2.614f)

Unless they happened to be part of a priestly college, however, elite Romans were almost exclusively spectators of dances. Roman banquets often featured professional dancers - male, female, or both - who would perform carefully choreographed pieces for the pleasure of the diners. Spanish dancing girls seem to have been especially popular in the late first and early second centuries. Juvenal, with characteristic sourness, condemns those who indulge in such things:

"You may look perhaps for a troop of Spanish maidens to win applause by immodest dance and song, sinking down with quivering thighs to the floor..." (11.162-4)

Most Romans, however, seem to have had no problems with immodest dance or quivering thighs.

Outside of banquets, the Romans were very fond of watching pantomime, a ballet-like entertainment in which a highly-trained masked dancer (usually male) performed an episode from mythology as a stylized dance, to musical accompaniment. Pantomime was sometimes criticized:

"The pantomime dancer, [a Cynic philosopher] said, was a mere appendage to flute and pipe and beating feet; he added nothing to the action; his gesticulations were aimless nonsense; there was no meaning in them; people were hoodwinked by the silken robes and handsome mask, by the fluting and piping and the fine voices, which served to set off what in itself was nothing." (Lucian, Of Dancing 63)

But many appreciated the talent and range of the star pantomimes, who could imitate episodes from the madness of Ajax to the love of Venus and Vulcan to Saturn devouring his children (I would have liked to see that one).

Elite Romans, in short, knew and appreciated a great variety of dances; but they very seldom polished the dance floor themselves.