Standing armies are a relatively recent historical phenomina. Before them you had 2 things: the medieval system of lord/vassal military obligation & the pros — who were the mercenaries.
Medieval lord/vassal relationships eventually got so complicated that the king could never be sure who would show up when the call came (blood relationships were increasingly tangled). But as long as the king had the coin, he could always rent a competent military force for the duration.
To a large extent, standing armies came about, in many countries, because the king needed to break the back of the nobility. As you mentioned, relying on the nobles to bring their vassals to war was very vulnerable to politics- if a Count or Duke decided he wanted to switch sides and abandon his king, he could take his troops to the other side and cripple the king's ability to fight a war. A standing army, answerable to the king, went a long way towards limiting the power of the nobility.