I won't vote, since the choices are somewhat limited, but I'll make a list:
Medieval
The Army of William the Conqueror Normans, Bretons, & French, in a balanced force of heavy cavarly, infantry spearmen, and archers.
The Crusader Army of Richard the Lion-Heart A formidable amalgamation of both secular knights and fighting monks (Templars & Hospitallers), as well as German and North Italian crossbowmen, protected by infantry spearmen with large shields (pavesari). They certainly gave Saladin a bloody nose at Arsuf.
The Mongols The record of the Mongols speaks for itself. For all intents and purposes, they were unbeatable in the field. They also excelled at sieges, with the help of Chinese and Persian engineers, as well as the efforts of Georgian and Armenian auxilliaries, etc. Aside from the successful defense of the Hungarian town of Szkesfehrvr (aka Stuhlweissenburg) by a band of Italian mercenaries, the Mongols defeated virtually every European force they encountered. They likewise had tremendous success in the East. Their only real failures were against the Mamluks at Ayn Jalut, and against the Vietnamese. I don't count the two invasions of Japan because the "Mongol" forces involved in both campaigns were made up mainly of Chinese and Korean auxilliaries, and it was in any event the weather which ultimately did the fleets in.
The Mamluks They beat the Mongols--'nuff said.
English yeomen (longbowmen and billmen) The English yeoman was a formidable fighting man. Known mainly for his use of the dreaded longbow, he also gained notoriety with the fearsome bill, a polearm with agricultural origins (used for pruning trees) that developed into military forms. Aside from archery, traditional English martial arts included fencing with sword-and-buckler (common sidearms for longbowmen and billmen alike), and the use of traditional polearms like the "short staff" (aka quarterstaff) and bill variants ("black bill", "brown bill", and "forest bill"/"Welsh hook"). The English gained most of their notoriety by repeatedly trouncing the French, but they also served as mercenaries throughout Europe--in Italy, Spain, etc.
North Italian & German crossbowmen see entry on Richard the Lion-Heart above.
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Medieval/Renaissance
Swiss Reislaufer The Swiss really helped to put footsoldiers back on the map, with their use of traditional weapons like the halberd (helleparten and pike (SpieB. The smashed the Burgundians, Austrians, and others, before turning towards mercenary employment. They were considered the very best infantry in Europe in the late 15th century, and they were so good that they prompted the Germans to simply copy them, when the first band of landsknechte was founded in the late 1400s. Imitation is the sincerest form of flattery... 
German Landsknechte The landsknechts ("servants of the land") were established in imitation of the Swiss, and it took them a while to get as good as the freedom-loving mountaineers. The Germans placed a greater emphasis on the use of firearms, which were used by some of their elite doppelsoldner (other doppelsoldner fought as close combat troops, with halberds and zweihanders--huge two-handed swords). Whenever the Swiss and Germans clashed, no quarter was given--this was considered "Bad War". Eventually, however, the landsknechts surpassed the Swiss--the Battle of La Bicocca in 1522 is usually considered the turning point. This was the first time the landsknechts soundly defeated the Swiss. The great German commander, Georg von Frundsberg (aka the "Father of the Landsknechts") even met the Swiss Captain of Unterwalden, Arnold Winkelried, and slew him with his pike.
The landsknechts continued to be a formidable force at least through the mid-16th century, but after that, the role of Top Dog went to the Spanish.
The Spanish Army of Italy, under Gonzalo de Cordoba The "Great Captain" was certainly an awesome commander, and he laid the foundation for the later successes of the Spanish Army. The original Spanish Army that invaded Italy in 1495 to counter the French was made up mostly of light cavalry (jinetes), as well as infantry sword-and-target men (referred to most commonly as rodeleros--"shield bearers"--but sometimes simply called espadachins--"swordsmen"). This force proved incapable of dealing with heavy French gendarmes and Swiss pikemen, and Cordoba suffered his only defeat that same year, at Seminara. Cordoba then fought a guerrilla campaign, until he could reorganize his forces. He introduced the arquebus on a wide scale, and 2,000 landsknechts leant to him by Maximillian added a much-needed pike element to his force (and eventually, the Spanish learned the Swiss-German pike drill themselves). The rodeleros were retained, but in smaller numbers. With this new infantry organization, Cordoba was never defeated again. Supported by friendly pikemen, the rodeleros were able to execute great carnage with their swords against the Swiss. He beat the French and Swiss time and again--at Barletta, Cerignola, and the Garigliano River. His reforms led to the establishment of the colunela in 1505.
The Spanish Army of Flanders, late 16th century With the ever-increasing use of firearms, the Spanish revamped their organization yet again, with the tercio in 1534. This was predominantly a pike-and-shot unit, though rodeleros were still occasionally used for specialist roles. With the tercio, the Spanish gained the most fearsome reputation in Western Europe, and the Spanish Army of Flanders was probably one of the two very best armies in the world at that time (the other one was the samurai army that Hideyoshi sent to Korea in 1592).
The Samurai Army of Hideyoshi, late 16th century In the 1540s, the Japanese were first exposed to the matchlock arquebus by the Portuguese, and the were understandably impressed. They built copies of this weapon in droves, until they supposedly ended up with more firearms than existed in Europe! Like other warrior cultures with a strong archery tradition (the English, the Venetians, and the Ottoman Turks), the Japanese integrated the use of guns and bows nicely--archers were used to provide covering fire for the gunners while the latter reloaded. Although they failed to hold onto Korea (let alone conquer Ming China, as per Hideyoshi's plan), the Japanese in the 1590s nevertheless demonstrated their power over those six horrible years of the so-called Imjin War.
Peace,
David Black Mastro
Edited by Landsknecht_Doppelsoldner