Charlemagne had himself crowned Emperor, pretending equality with the Byzantine ruler and continuity with the Roman tradition. How legitimate was this? Were the Franks just pretentious barbarians or did Charlemagne's empire represent a rebirth of civilzation in Western Europe?
By having the Pope crown him Emperor, two political objectives were accomplished.
Firstly, as others have posted, it established him as the official "Emperor." Even though it was only in title, it legitimized his creation of the Carolingian Kingdom, hearkening back to the days of the Roman Empire. Interestingly, in one form or another, the Western "Roman" emperor was an office that lasted until 1804, a thousand years after it was started.
Secondly, it re-enforced the reciprocal powers of the Church and State, which expanded the feudal caste system. The secular power acknowledged the legitimacy of the spiritual leader of the West, and the spiritual leader of the West acknowledged the temporal power of the Emperor. This synergy created by these respective offices brought Europe to the threshold of the Mediaeval Era. Although only a vestige of its former importance, even today royalty are crowned by clerics.
Whether Charlemagne was "self-crowned" is debatable. In the Roman Council of 800, Pope Leo and the dignitaries of the Church that since Charlemagne held Rome itself, the site of the emperors of this kingdom, it was only fitting that he be crowned emperor.
Since almighty God had put all these places in his power it seemed fitting to them that, with the help of God, and in accordance with the request of all the Christian people, he should hold this title.
According to one historical record, King Charles did not wish to refuse the council's petitiion. He, therefore, "humbly" submitted himself to God and the cardinals and pope and became emperor on Christmas Day, being consecrated by Pope Leo.
Charlemagne's territory was not as vast as the Roman Empire, but it was still immense, including all of modern France, marchlands in modern Spain, all of northern Italy, and most of modern Germany. He also instituted a flowering of culture founded on that of the Romans. He built cities and roads, encouraged learning, and facilitated He was certainly attempting to connect himself to an ancient tradition by crowning himself Emperor of the Romans, but it is probably incorrect to call him a barbarian.
Most historians do see Charlamagne as a very important figure in the history of the west, not simply for his military achievements but perhaps even more for his cultural legacy. He was an intelligent man who appreciated learning and who did indeed help foster a kind of cultural renaissance.
Charlemagne was certainly not a barbarian by Middle Age standards. He initiated a rebirth of art and culture (known as the Carolingian Renaissance) throughout the lands he ruled, and he eventually became the founder of the modern areas of France and Germany, earning him the moniker "father of Europe."
Honestly, I think that Charlemagne was trying to bring about a certain amount of continuity. After the sacking of the Roman Empire, he might have felt he had earned the right. It may seem strange that you can destroy a culture and then want to emulate it, but at its height the Roman Empire was admirable.
Charlemagne was attempting to demonstrate, in a very visible as well as symbolic manner, that he was the person with the ultimate power and authority. If someone else had put the crown on his head, that would have given that person a position over Charlemagne that went against everything he was trying to establish.
Pretentious, but not barbarian. By the time of Charlemagne, the Western Roman Empire was long in the past. Therefore, it would be pretty hard to take the idea of continuity seriously. In addition, Charlemagne did not control anywhere near the amount of territory the Roman Empire did nor did he hold it anywhere near as securely. So crowning himself was pretentious but understandable as an act of propaganda.
There are of course two sides to this. On the one hand, it was rather pretentious, as he didn't control the same kind of territory as was controlled under the Roman empire. On the other hand, his achievements were remarkable in terms of the territory that he did gain power over and the kind of impact this had on culture.