Absolutely loads! Europe has been inhabited for well over 5000 years, and Christianity has only existed for the past 2000. So if you think of any of the civilizations that existed before the year 1CE, then you can start to get an idea of the number.
If you'd like to know the most famous ones, then I'd say:
Ancient Greek religion, gods such as Zeus and Ares, and heroes such as Herakles.
Ancient Roman religion, drew heavily from Greek religion, as well as Etruscan (Pre-Roman Italian civilization) religion.
Celtic religion, made famous from the works by Julius Caesar, famously used human sacrifice
Norse religion, the Norse worshipped their own gods until Scandinavia was Christianized from the 8th - 12th centuries. Famous Gods include Thor and Loki (Thank you Marvel), and many of their gods still remain in English as days of the week (e.g Thursday = Thor's Day)
Judaism also existed in Europe, as indeed it still does today.
With the exception of Judaism, most of these religions were Polytheistic, and often had an emphasis on communal public worship, and sacrifice (either of animals or humans) as an offering to the Gods.
But this barely scratches the surface, of what is an enormous topic, if you have any more questions (be them more specific or not) feel free to ask. Also, have a look at the [Ask Historians FAQ] (http://www.reddit.com/r/AskHistorians/wiki/faq#wiki_religion_and_mythology), there's a subsection on religion, and you might find some more answers there.
This is a pretty problematic question to ask because pre-Christian beliefs can not be as easily categorized as we moderns would like. While there was a variety of traditions in pre-Christian Europe, it would be a mistake to construe them, as the poster above has, as a collection of unified religions akin to Christianity or Islam. In my opinion, the way most of us today conceive of pagan religions is largely informed by our perceptions of Abrahamic belief structures. Pre-Christian faiths were not uniform; their gods had no consistent meaning to all adherents, they had no central dogmas or tenets, their beliefs and figures were frequently in flux and influenced by neighbouring traditions.
There is also a question of the extent of devotion: there is reliable evidence which suggests that belief structures centered around agrarian life predating the Indo-European structures existed until the medieval era (whether they were a direct survival of the Neolithic or a general expression of agrarian consciousness is contentious). These pre-pre-Christian beliefs were focused around the use of magic to manipulate the material world, usually for purposes like ensuring the fertility of crops, but were reflective of an entire consciousness based around man;s capacity to influence the world through magic because both were made up from like materials. Just as many medieval peasants were ignorant of the intricacies of the Christian faith, it is likely that most pre-Christian agrarians would have been ignorant of the entire pantheons of gods and corpus of myths that we attribute to their religions.
Even regionally, general constructions like the quote-unquote (my keyboard switched languages and I havenèt figured out how to fix it yet :P) Celtic religion do not stand up. For example, although we can identify the presence of figures called druids in both Gaul and Ireland, there is no evidence that suggests that Irish druids held the exact same social functions or that they practiced the same beliefs as the the druids of Gaul, as described by contemporaneous Greek and Roman writers. While Classical writers stress the Gallic belief in the transmigration of souls upon death, there is no indication that such belief ever existed in Ireland. Likewise, while contemporary sources suggest that sun-worship was an important feature of pre-Christian Irish belief, no evidence that I am aware of suggests that the Gauls worshiped the sun.
So, as you can see speaking of pre-Christian religions as unified entities is largely problematic. To answer your question more directly: while there were larger cultural-pantheons, pre-Christian belief, especially in temperate Europe, would have been overwhelmingly localized. It would be impossible to enumerate the countless regional and local variations or interpretations of these larger traditions of belief.