I've looked at the threads in the faq, but they don't really address my particular question. I understand the appeal of Christian doctrine to the masses. So it makes sense that certain pagan or non-christian societies would convert (i.e., it would be specifically endorced by the upper classes) once enough of the peasantry had converted. I take this to be roughly the situation in the Roman Empire, but I'll be happily corrected if I'm wrong.
I'm more interested in those cases where the leaders seem to have converted first. As in the case of the Vikings. Presumably there are other cases of missionaries in the 17th and 18th centuries as well. What was the appeal of Christianity to kings or chiefs?
I highly recommend reading The Rise of Christianity by Rodney Stark. As an agnostic writer, he didn't believe the Holy Spirit was responsible for the spread of Christianity (as the standard Christian narrative goes) and used his sociology studies on the spread of new religions in modern times (the Moonies, etc.) to shed light on why Christianity was successful.
once enough of the peasantry had converted
While you are paraphrasing the standard narrative, he shows it probably was the other way around, with well-to-do Roman women being the earliest, most common, and most influential recruits into the church. This is based on a variety of evidence, including the relative number of women's and men's outfits found at dig sites in very early churches: there were far more women than man. So much so that Pope Callistus I (~220AD) approved of upper class Christian women becoming concubines to upper class Roman men, because they simply did not have enough men in the church to marry, and marrying out of class was unpalatable to most of them. Christianity appealed to women for a variety of reasons, not the least because it held women with greater respect than most cultures and religions did at the time.
This sounds paradoxical to us looking back at it from the 21st Century (since we "know" how patriarchal the early Church was), but the patriarchy was due to men following the women (as men still do today at nightclubs) into the Church, and eventually displacing them. By St. Augustine's time (~400AD) it was firmly patriarchal, and women were eventually prohibited from church leadership and theology. (What women am I referencing? See for example Priscilla, and Phoebe, and Thecla.)
He also goes into the aspects of Christianity that caused it to succeed where other newborn religions fail, which I can detail for you if you're interested.
To Anglo-Saxon kings in England, Christianity was especially attractive because of the structures of the Church which came with it. Æthelberht of Kent was the first Anglo-Saxon king to convert in 597. Christianity brought with it the organisational hierarchy of the Church which formed the administrative basis of successive English states for the the rest of the period. Monks and clergy occupied the majority of bureaucratic roles in English courts, particularly as scribes. Documents such as charters and edicts and law codes allowed kings to administer far greater areas and to delegate provincial control. The king no longer had to be present in person to transfer land to his followers, uphold the law or oversee the collection of taxation or even to raise his armies.
The Church also brought attachments which were outstanding propaganda tools for transforming what were essentially warbands into legitimate kingdoms and bringing the English kingdoms into the European Christian community, and so greatly appealed to the ambitions of rulers. Patrongage of the Church was seen as continuing the traditions of Imperial Rome, the Church built in stone and wrote histories of the kings who supported it. England's first post-Roman legal code was written by Augustine of Canterbury on behalf of Æthelberht of Kent, thus establishing him as a king in true "Roman" tradition. Christian kings were encouraged to "convert" their pagan neighbours and act as their baptismal sponsors, granting them a level of spiritual authority over their subreguli. Christianity also enabled rulers to patronise monastaries as royal centres, often forming saints' cults to their own ancestors and thus increasing their legitimacy amongst their people. By the 890s, by which time England had been fully Christian for centuries, Æthelred and Æthelflæd of Mercia 'liberated' the bones of the Mercian martyr St. Oswald from Viking-held Bardney to Gloucester in order to establish it as a religious centre under their control, and to legitimise their hold as the rulers of Mercia given Æthelflæd's West Saxon ancestry.
Blair, John (2005), The Church in Anglo-Saxon Society, Oxford
Campbell, James (1986), ‘The Church in Anglo-Saxon Towns’ in Derek Baker (ed,), The Church in Town and Countryside, Studies in Church History 16, (Oxford, 1979), pp.119-135
Rollason, David (1989), Saints and Relics in Anglo-Saxon England, Oxford