War cries are attested in Classical literature as far back as Homer, one of whose standard epithets for Menelaus is βοὴν ἀγαθός, "good at the war-cry" (literally "good with respect to shouting," where βοὴν is the accusative of respect of βοή, "a shout, cry"). Greek's usual word for a war-cry is ἀλαλαί, which would have been repeated as the force advanced--the verb "to shout, raise the war cry" is ἀλαλάζω, which is onomatopoeic (and, amusingly, closely resembles the also onomatopoeic verb ἀλαλάω, "to render speechless"). In Attic the variation ἐλελεῦ was more common--several of Aristophanes' plays famously end with a mass celebration that includes the chorus raising the Attic war cry. But this is really just a variation based on the way the Attic dialect works. You'll notice that neither ἀλαλαί nor Menelaus' βοὴν ἀγαθός refer to any actually articulate (or in Menelaus' case, specific) cry. Menelaus just shouts, he doesn't actually shout anything in particular. That's pretty common in Greek and especially in Latin. Latin doesn't have a word for a war-cry, it simply uses clamor, which is just the word to describe any sort of shout. This, for example, is how Caesar describes both the shouts of his men at Pharsalus and the Gauls during their night attack at Alesia--of the Gauls he says subito clamore sublato, "with a sudden cry raised up," and of his men at Pharsalus he says that in a good attack clamoremque universi tollerent, "the whole body should raise a shout." That's more or less typical of Latin descriptions. In rare cases we see specific words being used. The de Bello Africo says that Caesar signo Felicitatis dato equo admisso in hostem inter principes ire contendit, "with the signal 'Felicitas' given and his horse let loose charged towards the enemy's front rank." Caesar's watchwords in particular seem to have invoked Venus frequently, which shouldn't be surprising. At Pharsalus Caesar's watchword was "Venus Victrix," from the name of the temple that he dedicated to her afterwards and Appian's remark that Caesar's watchword was Ἀφροδίτην νικηφόρον, "Venus Victrix" and that Pompey's was Ἡρακλέα ἀνίκητον, "Hercules Undefeated," presumably for Hercules Invictus, to whom Pompey had dedicated a shrine in his theater. But these are technically watchwords, not battle cries--they clearly could double as battle cries, but Caesar suggests that Pompey's men never actually shouted anything at all, which he famously criticizes since a single great shout in unison damages enemy morale and strengthens that of the attackers. But Roman war cries are confusing--Polybius says that the Romans beat their shields as is customary in their country (κατὰ τὰ πάτρια), but beating of shields isn't exactly prominent in Latin literature. Polybius also seems to think that the Romans have some sort of usual warcry, since he says that the Macedonians and Romans shouted their own customary warcries at each other at Cynoscephalae, but what the hell he's talking about I don't think anybody knows. Polybius does draw a contrast, however, between the unison shouting of the Romans at Zama and the disparate cries of the Carthaginians, whose contingents, he says, each had their own customs and who couldn't raise anything but an uncoordinated din. A final remark should be said, though, on what exactly a warcry is. Most of the warcries from Classical literature bear more resemblance to a Kiai or a signal--indeed, Caesar sometimes refers to warcries as being signa--than to what you might see in movies or the longish verse cries that Tolkien gives his characters, often a couplet or more. Is that what we mean by a warcry? Is it one or the other, or perhaps both? And then there's something of a grey area--what would a paean be?