Sigurd I, King of Norway has his journeys chronicled in the Heimskringla. While he campaigned in Palestine, he spent many years journeying to and from the Holy Land as a guest of various kings and emperors, travelling through England, Spain, Sicily, Constantinople, Bulgaria, Hungary, Pannonia, Suabia, Bavaria, and finally Denmark before returning home.

If the saga is to be believed, he was an honored guest of these courts and was often given sumptuous feasts and gifts. The Byzantine Emperor (Alexios I, I think) threw games in his honor. Lothair III, the Holy Roman Emperor, "received him in the most friendly way, gave him guides through his dominions, and had markets established for him at which he could purchase all he required."

Historians do debate the historicity of the Heimskringla, although the Saga of Sigurd and his brothers is towards the end of the book, it was still written some 100 or more years after the events described. As far as I can tell we can't discount the Norweigan Crusades actually occurring, though, and the journeys and monarchs describe make sense in that context.

Other than as part of a military expedition of conquest it was uncommon, but not unheard of. The example red-team gives below of a crusader king is a good one. The difficulty of travel and the instability of a monarch's grasp on power would have been major deterrents to leaving the home territory prior to the nation-state period.

A notable example of a meeting between heads of state in the pre-modern era was Henry VIII's meeting with Francis I at the "Field of the Cloth of Gold" in 1520. This meeting was to solidify the new terms of peace between the countries after years of war. The site of the meeting was English-held, located in modern French territory, and so was probably an effort at finding neutral ground. Henry and Francis met again in 1532. This is in contrast to some later monarchs, like George III, who never left the British Isles.

Another example of a pre-modern head of state visiting another country was John VIII Palaiologos, the next-to-last Byzantine emperor, visiting Italy in 1439 in an effort to rally western support for defending Byzantine independence from the Ottomans by trying to repair the rift between the eastern and western church. A notable result of this visit occurred because he was accompanied by Gemistos Plethon, a Byzantine scholar who did a great deal to introduce Classical Greek learning to the west.

I'm sure other examples exist, but these two are the ones I remember in particular. By the mid-19th century travel had become easier, allowing for more frequent contact between monarchs. Prior to this period most business was conducted via ambassadors, or correspondence.

In 1520 Henry VIII of England travelled to France to meet the French King Francis I ; an event that became known as the "Field of the Cloth of Gold" due to the splendour of the tent cities erected as each king tried to outshine the other. The two kings even wrestled (Francis won).

They were supposed to be discussing a treaty of peace (and maybe an alliance against the Emperor) but nothing came of it- they were back at war with each other as usual before long.

The important example is Russian Emperor Peter I. He went with Russian embassy to Holland incognito (though it seems everyone knew who he was) and used his time to research European navy, science and culture. He later sort of westernized Russia making it more similar to Western Europe culturally and created some institution (navy, academy of science) with invited Europeans.