One factor no one mentioned yet is that Christians were able to utilize the infrastructure of the Roman empire, whether we count roads and ports themselves, or relative peace inside its borders. That not only gives you enough people who can afford to preach (if you have too few, then they need to farm/warmonger/create goods), but also allows a scholarly/theological movements to begin.

Since Christianity became a state religion, spreading it became one of the tools to strengthen the Empire's unity (by, did that not work out at all, huh?), giving missionaries further support. By the time Empire definitely fell apart, Christian institutions such as monasteries remained one of the few organizations still standing, and monks and bishops were valued for their knowledge, being one of the few literate people around.

And to get access to all these literate, educated people, all you had to do was convert, which would also put you in good graces of kingdoms next to you (bishops and papal legates were very often acting as diplomats in smoothing out agreements between warring parties).

As for why Christianity was popular with the lower classes, only social security in middle ages came from them, they took care of the poor and old, ran the first hospitals and again, were literate. Priest in a village was more often than not the one who wrote letters when the village wanted to bring a matter to the attention of their lord, and people sometimes came to them for advice on legal matters.

According to Julius Caesar, the druidic religion / philosophy that he encountered in his conquest of Gaul originated in Britain and spread to the continent:

Over all these Druids one presides, who possesses supreme authority among them. Upon his death, if any individual among the rest is pre-eminent in dignity, he succeeds; but, if there are many equal, the election is made by the suffrages of the Druids; sometimes they even contend for the presidency with arms. These assemble at a fixed period of the year in a consecrated place in the territories of the Carnutes, which is reckoned the central region of the whole of Gaul. Hither all, who have disputes, assemble from every part, and submit to their decrees and determinations. This institution is supposed to have been devised in Britain, and to have been brought over from it into Gaul; and now those who desire to gain a more accurate knowledge of that system generally proceed thither for the purpose of studying it.

Whether this came about by cultural diffusion or missionary activity is unclear, but I'd err towards the former. Religious priesthoods seem to have been centrally important socio-political force in Northern Europe since at least the Neolithic and it's quite possible that the label of 'druid' might have originated in Britain and then simply have been applied to to pre-existing priesthoods of the various other Celtic speaking peoples (though this is not to imply that the druids existed since the Neolithic or whatever).

I would argue against a sort of unified 'church' of druidism because the priesthoods called 'druids' found in various Celtic speaking cultures seem to have served a variety of socio-political functions. In Ireland before the 4-5th centuries for example, society appears to have been organized in a sort of theocracy of competing cult-allegiances where the druids as a class probably held the most political power, while in Gaul, Caesar's narrative of his adventures there paints a picture of a society organized and controlled by a warrior-aristocracy divided into a number of monarchies and republics despite his claims of the druids' political primacy in that society in the very same text. Indeed, the druids are conspicuously absent from Caesar's account, where the primary Gallic antagonists and protagonists are all members of the warrior-aristocracy.

One might answer this question by comparing the structure and tenets of Christianity to other belief systems. As a revealed religion, it's a core conceit of Christianity that the Gospel was inaccessible before the arrival of Christ and that the message must be spread to everyone. The religion itself seems tooled to grow itself.

When we compare Christianity to the collection of beliefs and practices we might associate with Greco-Roman or Egyptian religion, we can see stark differences. In these other religious systems there is less claiming access to ultimate Truth and less entreating to spread a particular religious view or practice. The Romans were cosmopolitan about religion for the most part - they absorbed new practices and folded them into a wider spiritual system in which the traditional 'ethnically Roman' religion existed alongside various mystery cults and worship of foreign deities. Christianity was accused by the Romans of being atheistic because it was revolutionary in denying the existence of other deities and was accused of being hostile to the Roman state and religion.

Christianity differs significantly from various Pagan beliefs and practices in that it is quite self-consciously defined by it's differences from other religions (e.g Judaism), it's focus on evangelism and its' universal applicability, and also its emphasis on being saved. I think this makes Christianity rather unusual as a religion.

There was at least one pagan religion that did spread: some parts of the pantheon which we think of as Graeco-Roman had a proto-Indo-European origin, and got as far as Scandiavia. So for instance Dyeus = Zeus = Diespiter = Jupiter = Tiw = Tyr.

Could anyone comment on the means by which this spread?

Do you consider Buddhism pagan ?