Reigning monarchs tended to stay in their kingdoms so that they could rule effectively. Leaving for extended period of time was potentially very dangerous. Appointed regents may be incompetent or unpopular, rival claimants could make an appearance, and vassals hungry for power could make political moves. For an example of such chaos just look what happened when Richard I left to join the Third Crusade. Despite making arrangements to avoid this, Richard's brother John returned and led a revolt, while the regents Richard had appointed hated one another and did not govern well at all.

However, many monarchs were well traveled. They usually did their traveling before their reign however. Pilgrimages to Rome or other holy places were fairly common. Reigning monarchs also tended to accompany their armies on military campaigns, the Crusades being an example that would take them farthest from home.

Perhaps the most well-traveled monarch in the 11th Century was Harald Hardrada, King of Norway. Born in Norway, he traveled through Sweden to live in exile in Russia. There he became a general for their ruler Yaroslav the Wise. He led armies against the Poles and possibly also the steppe nomads of what is now southern Ukraine. He later joined the Byzantine Varangian Guard in Constantinople. With the Varangians he led campaigns in the Mediterranean, in Turkey and Iraq, Jerusalem and Sicily, primarily fighting against the Arabs. When he returned to Norway and became king, he led an invasion of Denmark, and was finally killed at Stamford Bridge during his famous invasion of England.

Traveling long-distance doesn't seem to have been as unusual as people thought in the middle ages, at least not if you were part of the upper aristocracy, probably the top 5% or so of society. As has already been mentioned though, it's probably more likely that you would travel more if you weren't a king, as being a king kept you pretty busy in your own kingdom.

Around the year 1000 though, you would usually have only traveled when you had a reason too. The most common sort of travel would have been in the course of normal politics. As a wealthy aristocrat, it's your duty to advise and counsel the king, and so you would travel on a fairly regular basis around the kingdom to attend his court, appeal to him for judgement, petition him for gifts or grants of land and generally to be a player in the political life of the kingdom. How much of the world you got to see would depend on which kingdom you lived in - a Scottish nobleman would naturally see less in his regular travels than a German duke or count whose King/Emperor spent half his time in Italy.

The second main reason to travel would have been to serve in war. This is obviously very dependent on where the war is at the time, but many German nobles would get to spend lots of time in central Italy throughout the 10th and 11th centuries, Scandinavian warriors found employment as mercenaries from Constantinople to Ireland and from the end of the 11th century the Crusades led to plenty of excuses to go fight in the Levant.

The final reason, and probably the one for which we have the most evidence, is to go on pilgrimage. Pilgrimage was a big deal in the middle ages, with universal pilgrimage cites such as Rome, Santiago de Compostella and Jerusalem attracting thousands of pilgrims a year. We know of literally hundreds of individuals who made journeys to these sites across the Middle Ages and most of these would have been very well off, since travel was dangerous and expensive. But since all travel was by ship, foot or horseback, you did get to see an awful lot more of the world traveling back then than we do now, jetting from one place to another in a big metal sky tube. So if you were Donnachad mac Briain, King of Munster in Ireland, who traveled to Rome to retire and die in 1063, you would also get to see big chunks of Britain, France and Northern Italy. Fulk Nerra, Count of Anjou, who went on pilgrimage to Jerusalem four times between 1003 and 1038: he would have passed through much of France and all of Italy at least, and probably visited ports in Greece, Anatolia and the big Mediterranean islands on the way. Even relatively no-name people could make these journeys - it's said that the first Norman knights who arrived to conquer Southern Italy in the 1040s were passing through returning from Pilgrimage when they saw the chance to carve out kingdoms for themselves.

So, while, yes you are incredibly privileged to travel in a safe, quick and comfortable modern fashion, the well off in the 11th century could certainly travel farther, if not particularly often, than is commonly assumed.

While not a ruler, Ibn Battuta is a great example of travel in a pre-industrial era. This map is an enormous undertaking in the modern era with modern transportation -- before the invention of the railroad, nevermind the airplane, it is frankly amazing that he was able to travel so far afield. And he was often received as a visiting dignitary by local sultans.

Hardrada was mentioned by another user and he's a good example. He, however, did the vast majority of his traveling before becoming king.

A good example of a ruler traveling is probably Musa Keita I of Mali (who you may know better as "Mansa Musa"). As a devout Muslim, he was obliged to undertake a hajj (pilgrimage to Mecca). And travel he did. His pilgrimage involved so many retainers, and he brought so much gold, that he appears to have sparked off run-away inflation in places. His trip, using modern roads, would take about 16,000 kilometers (counting the return leg). If you drove 60 mph for 8 hours a day, every day, it would take 20 days to make that trip. That's quite a road trip.