Poets and Teachers
These purveyors of words aren't central to any of the play's action, but they do stand out because of how widely they're disregarded, even when they have important things to say. While Shakespeare's work was considered important enough to get him royal patronage from King James I, poetry during Caesar's time was decidedly different. The most important pieces of literature from that time, whether poetic or not, focus on history and tradition. Livy's History of Rome, Caesar's own Gallic Wars, Tacitus' Histories, and Virgil's Aeneid had history at their core. The idea of writing for writing's sake wasn't popular.
Within that context, the presentation of the men of letters in Julius Caesar makes a little more sense. The first and only person who can explicitly warn Caesar in detail of the plot to kill him is a teacher of rhetoric, Artemidorius. Caught up in his affairs of state, Caesar ignores this learned man's teaching, which costs him his life.
Next we see Cinna the poet torn to shreds for having the wrong name. Even after the mob realizes he's not that Cinna, they kill him anyway as punishment for his "bad verses." (That the mob is ignorant enough to be this blood-lusty casts some doubt on whether they're qualified to be literary critics.)
The final poet we encounter shows up outside Brutus and Cassius's tent after their quarrel. He asks them to love each other as brothers and suggests that they shouldn't be alone together. (Probably a good idea, considering that they almost killed each other.) The poet points out that he has lived longer than they have and might have something to teach them. They just laugh at him, threaten him, and finally dismiss him.
In all three instances, men of words seem pretty randomly inserted into the play. There's no real reason to have a scene solely devoted to killing Cinna, or for the strange little exchange with the poet at the end. None of those instances move the plot along.
But think about it: Shakespeare is a writer. He can't just insert important poets into history, but he can do his best to argue within the play that poets and learning should be central to politics. The poets we meet are on innocent and important missions, all of which are deterred or slighted with not-so-awesome results. So perhaps Shakespeare is suggesting that men of state should also be men of learning; to ignore poets and what they have to teach is to court doom. It's a jab against both ancient Rome and Elizabethan England, but mostly it's an example of Shakespeare using a little of his own influence to promote his craft.