Honestly, there's no real point in this list; comparing generals of different times is silly in that their tactics (at the very minimum) were time-sensitive. However, I'll fire off the list of Great Captains and then my own personal favorites:
Cyrus II (Persia) - Created the first real World Empire (the Achaemenid one) and pz0wned the Lydians in the first real examples of battlefield maneuver.
Epaminondas (Thebes) - The guy who invented battlefield concentration, oblique order, and the top Greek general of his day. If he hadn't died at Mantinea (362 BC)...
Philip II (Macedon) - He created Alex's tactical instrument and "unified" Greece. He had a good chance of doing exactly what his son did, except he wouldn't have died so young. The Battle of Chaeronea is one of the world's most significant battles.
Alexander III (Macedon) - Alex the Great. No real explanation needed.
Hannibal Barca (Carthage) - Again, he has been gone over ad nauseam by the others on this thread.
Scipio Africanus Major (Rome) - Beat Hannibal at his own game, and helped the Romans beat the Seleucids at Magnesia, too. 'Nuff said.
Gaius Marius (Rome) - Came up with the highly influential Marian reforms, which ensured Roman survival and also the transformation into an official Empire.
Julius Caesar (Rome) - Again, not much to say here.
Belisarius (Rome) - People on the thread have talked about him a lot already as well.
Heraclius (Rome) - Beat the Sassanids singlehandedly from the Bosporus to Isfahan, and came up with the thematic system that would later save the Empire.
Genghis Khan (Mongols) - Too many people like to talk about him.
Dom Affonso de Albuquerque (Portugal) - Came up with the idea of modern naval strategy (securing bases to control sea routes, etc.) and, with Almeida, developed the long-lasting Portuguese Indian Ocean naval empire.
Francis Drake (England) - For his tactical innovations.
Hernando Cortez (Spain) - Conquered the Aztecs. 'Nuff said.
Alexander Farnese (Spain) - Managed to keep the Spanish Netherlands from splitting off and held his own against Henry IV.
Gustavus Adolphus (Sweden) - Already been gone over.
Henri de la Tour d'Auvergne, vicomte de Turenne (France) - Louis XIV's instrument of continental conquest. Beat Conde, Montecuculi, and William III consistently (the first only in the Fronde, of course).
John Churchill, duke of Marlborough (England) - Basically won the War of Spanish Succession for the Allies (though it was technically a tie, England got lots of free stuff at Utrecht).
Frederick II (Prussia) - Probably the greatest tactical genius in history. 'Nuff said.
Napoleon Bonaparte (France) - People have already spoken about him.
Horatio Nelson (England) - Another Drake. 'Nuff said.
Robert E. Lee (USA/CSA) - Played an important role in the Mexican War, and kept the CSA alive (if on life support) for four years.
Helmuth, Graf von Moltke (Germany) - The formulator of the modern general staff system.
My personal faves are Frederick and Alex, with Epaminondas and Napoleon going pretty close to that. Patton was not suited to anything above army-level command, which is not necessary to be demonstrated. Rommel shouldn't have had command over anything over a division (and even then, look at what happened at Arras in 1940!). Sherman wasn't bad at all, but not a Great Captain. Washington, again, is not of unbelievably high caliber, but is probably in the top fifty. Monty was just a fool, and was a World War I general in a war far too advanced for him.
Had I more time available, I would write more, but alas, I have an errand to run.
