It beggar'd all description

All that and a barge of pimps

The same man who efficiently convinced a town square full of ornery, confused Roman citizens that Julius Caesar was a great man, tragically cut down by "honorable men," had absolutely no chance when he went to Egypt. His clever, sharpened mind couldn't get a word in edgewise to his goolies the moment he saw the incomparable Queen Cleopatra. And really, no one can blame him. Antony's fellow triumvir Octavius tries, yes, but the fact that Enobarbus--Antony's crusty and sarcastic wingman--delivers one of the most sensuous, poetic descriptions of a woman ever penned by the human race is testament to Cleopatra's historically infamous powers of consummate seduction.

No one actually approves of Antony's "gyptian" affair (except Antony and Cleopatra themselves, who are having the time of their lives partying like the whole of Egypt is on an endless Spring Break). But the play displays such an extraordinary aura surrounding this most powerful and uncompromising of Shakespeare's women that it's a true wonder the original player who portrayed her was just a young boy in drag. 

From a memorization standpoint, it's one of the easier speeches to get down. The imagery is rich and beautiful, full of details that create their own "mind palace" mental map of its verbal progression. Imagine being amongst friends at a party, drink in hand, keeping their attention with a lurid story about a recent vacation you had. That's essentially what Enobarbus does.

In this scene, Caesar and Antony are in Rome, discussing Antony's recent sexual fugue in Egypt. Caesar hopes to curb Antony's unrestricted behavior by marrying his chaste sister off to Antony. As soon as the big men leave the room, Enobarbus and his buddies start talking about his time in Alexandria. They all want to know if the stories about Cleopatra's beauty are true, and Enobarbus really works the room with his little story of how Antony met her. Obviously, this speech leads the men into a bawdy conversation about Antony's bedroom exploits.

Antony & Cleopatra, Act II, Sc. II
Enobarbus: I will tell you. 
The barge she sat in, like a burnish'd throne, 
Burn'd on the water: the poop was beaten gold; 
Purple the sails, and so perfumed that 
The winds were love-sick with them; the oars were silver, 
Which to the tune of flutes kept stroke, and made 
The water which they beat to follow faster, 
As amorous of their strokes. For her own person, 
It beggar'd all description: she did lie 
In her pavilion--cloth-of-gold of tissue-- 
O'er-picturing that Venus where we see 
The fancy outwork nature: on each side her 
Stood pretty dimpled boys, like smiling Cupids, 
With divers-colour'd fans, whose wind did seem 
To glow the delicate cheeks which they did cool, 
And what they undid did...

Her gentlewomen, like the Nereides, 
So many mermaids, tended her i' the eyes, 
And made their bends adornings: at the helm 
A seeming mermaid steers: the silken tackle 
Swell with the touches of those flower-soft hands, 
That yarely frame the office. From the barge 
A strange invisible perfume hits the sense 
Of the adjacent wharfs. The city cast 
Her people out upon her; and Antony, 
Enthroned i' the market-place, did sit alone, 
Whistling to the air; which, but for vacancy, 
Had gone to gaze on Cleopatra too, 
And made a gap in nature.