You might want to look at the World of Legends modpack for some really nice unique units (
http://forums.civfanatics.com/showthread.php?t=348162). I made a list of the ones for cultures that aren't currently in the mod:
Americas:
Venezuela: Llanero. Cavalry with Guerrilla I and Woodsman I.
Europe:
Austria: Jaeger. Rifleman with +1 first strike chance and immunity to first strikes.
Hungary: Hussar. Cuirassier with Commando and March.
Italy: Condottieri. Cuirassier with +50% city attack/defense.
Poland: Winged Cavalry. Cuirassier with +50% vs. melee.
Africa:
Berber: Libyan Warrior. Javelineer with +1 Strength.
Hausa: Savannah Cavalry. Cuirassier with Blitz.
Nubia: Kuhorsehockye. Archer with +1 first strike chance and +10% city attack/defense.
Kongo: Levy Archer. Longbowman with +50% vs. melee.
Swahili: Dhow. Caravel with -20 hammer cost (total -50%) and with Flanking I.
Middle East:
Armenia: Nakharar. Horseman with 1 first strike chance and Leadership.
Minoan: Palace Guard. Warrior with +1 Strength.
Phoenicia: Colonist. Scout with +1 Strength, can attack, and starts with Sentry I.
Turkmenistan: Turcoman Rider. Knight with -1 Strength and +100% city attack.
Uighurstan: Nomad. Horse Archer with Guerrilla I and +20% withdraw chance.
Asia:
Chola: Kallarani. Maceman with +25% city attack and defense.
Vietnam: Marine Infantry. Maceman with Woodsman II and 1 first strike. Could also use the Legends of Revolution (
http://forums.civfanatics.com/showthread.php?t=319235) Viet Cong. Infantry with 2 moves, ignores terrain cost, and ignores building prerequisites. (Legends of Revolution is big on having building prerequisites for units. Infantry requires Barracks without Military Tradition and Factory before the Modern Era.)
Two others I thought up:
Texas Rangers. Culture (Texan) requires Culture (American) and Horse. Not sure on a tech requirement. Cavalry equivalent with Sentry I and Riot Control V. A mobile police force.
Nepalese Gurkha. Culture (Nepalese) requires Peak. The unit would be a Musketman or Rifleman equivalent with Guerrilla I and Fanatic.