What would happen to me if, while living in Europe, say, in the 13th or in the 15th century – in fact, in any time of the existence of the Roman Catholic Church before the Reformation – I openly declared that I didn't believe in Christ or in the existence of God. What consequences would I have been facing then?
You would have been excommunicated by the church and shunned by the community. But then again, for some individuals, the solace that comes from "having the courage of your convictions" and "being right" may have made that option more palatable (see de Tocquville below).
People would have thought you odd, and possibly a public health hazard. (After all, God could punish the village for your unbelief.) But, if you were willing to move, you'd probably have been ok.
There were all sorts of dissenters - Waldensians, Hussians, Huguenots. When they became large enough to threaten the local potentate, sure, you'd be dealt with- but the fact that these groups could begin to number in the tens of thousands shows how tolerant the High Middle Ages could be.
Sociologically speaking, the community simply cared about other things far more - surviving the Plague (1347 - 1350), resisting invasions (When Genghis Khan invaded Poland in the 1240s, people thought the world was coming to an end!), ignoring the Papal politics of your time. Heck, for at the least the latter half of the 14th Century, you had three Popes to choose from. They were so busy fighting amongst themselves, they would have had little time for you. And, if you were a peasant, you were either so busy trying to make a living (before the Black Death) or choosing which of several jobs you wanted (after the Black Death), religious conformity would have been low on your list.
Duns Scotus, for example, was able to get away with chipping away at the ecclesiastical authority of the Pope pretty signficantly - and he prospered.
It is unlikely that you would have been publicly "executed" - you just would have been so weird that nobody else would have wanted anything to do with you.
In other words, while you may have been anti-Christ, you certainly weren't "the Anti-ChristTM". You were just a nut!
Incidentally, as Alexis De Tocqueville (Democracy In America) points out that your persecution at the hands of a despot would have entitled you to take solace in your martyrdom. In contrast, simple ostracism may seem a greater punishment, if only because you would have realized how different and alone you truly were. All that said, if you were truly an atheist, your love of reason should have been sufficient solace for you not to care.
The inquisitors official purpose for inquisitorial penalties (which were torture, imprisonment, and not uncommonly, death)
quoniam punitio non refertur primo & per se in correctionem & bonum eius qui punitur, sed in bonum publicum ut alij terreantur, & a malis committendis avocentur
for punishment does not take place primarily and per se for the correction and good of the person punished, but for the public good in order that others may become terrified and weaned away from the evils they would commit
So the inquisitions were absolutely aimed at serving as an example; if your beliefs were not in agreement with the local church, you were by definition heretical, and would have been at risk, without doubt. A vocal and proud non-believer would make a fine example. Many labelled as atheist were targetted for legal persecution, continuing the tradition of earlier times.
Add to that, as Affable Geek rightly notes, you were likely to be shunned from family, friends and society (although I outright reject his conclusion that an atheist would "not care" about this - in a violent, hard and outright hostile time, where there wasn't easy and anonymous access to services such as buying food, affiliation in a society was even more important; an outcast is not likely to fare well).
Of course, in many cases punishment was in part political in addition to religious; if you were challenging the local officials (by encouraging people to think, always dangerous). Add to this that royal authority etc was usually "by divine right" - thus: by rejecting the faith you are undermining the local rulers, which was not well tolerated. If you think politics and religion are intertwined now... it was worse.
Also, at this point the word "atheist" is usually applied as an insult, applied to things such as different religious beliefs, suicides, and immoral people. The term itself (in everyday usage) didn't really mean the same as it does today (i.e. not believing in a supernatural deity). It was held as a threatening position (to society) by Thomas Aquinas, and even those in favour if religious liberty (John Locke, Thomas More) excluded atheists in their considerations.
Summary: it would not have ended well. Your best option would have been to disbelieve quietly.
A noted scholar of Christianity, Alec Ryrie, in his lecture "How to be an Atheist in Medieval Europe" points out unbelief was not a hypothetical situation in Middle Ages. Though it's worth noting that those of the period did not define unbelief merely as "denying the existence of God" as some do today, and as may be a premise of the question.
See YouTube’s video: How to be an Atheist in Medieval Europe (9:34).
It has been suggested that atheism in pre-modern times is simply impossible. In one sense this is obviously true, in the sense that the Greek word atheos... doesn't make its way into Latin until 1501...The word atheist first appears in English in 1553...When medieval and early modern Europeans talked about atheism or unbelief those words had a much larger range of meaning than they do for us now. As well as actual denials of God they include what was sometimes called practical atheism, that is, living as if you do not believe there is a God.
One person who fits this broader definition of unbelief according to Ryrie was Machiavelli. While Machiavelli was "not openly trying to subvert Christianity" (How to be an Atheist in Medieval Europe 40:08), he mused in some places about replacing Christianity--which he suggested elites should at least "cynically" endorse without regard for its truth, according to Ryrie--with something more "manly" and useful to the state for political purposes 41:45. This is a clear example of "practical atheism" as we might find in that period.
Now, was Machiavelli punished for his unbelief? No. He was tortured and forced into exile by the Medici, but his unbelief seems to have had nothing explicitly to do with it. His political fortunes waned instead. So we have at least one case of someone professing unbelief pre-Reformation in Europe--as it was understood by those of his time--not being explicitly punished for it.
See Wikipedia’s article on Niccolò Machiavelli.
What is an open atheist's fate in the Middle Ages in Christian Europe?
As well as the above answers are, they may or may not be all that accurate.
For one thing, Affable Geek’s answer as good as it is lacks any historical evidence and to some degree relies on his personal perspective or opinion.
First of all, to be excommunicated from the Church, one has to have been a baptized member of the Church. A non-baptized person who professes to be an atheist, can not be excommunicated from the Church. Could they shunned by others: possibly.
Forced conversions are not valid. Even the Inquisition recognize this point.
Chances are that what would happen to a professed atheist would depend on where he lived.
Chances that a truly professed atheist, who quite openly admits it, would simply be allowed to live his life out as best he could, unless he publicly blasphemed one of the sacred dogmas of the Church or their saints or worse yet God himself. If it dealt with an atheist who lost his faith, the faithful no doubt would pray for his faith to return.
Many canonized saints have suffered the dark night of the soul, where the very existence of eternity was strongly doubted. Souls, whether Catholic or atheistic must work towards their own salvation. The Church punishments would be in cases where genuine blasphemy has occurred only.
The atheist, like a believer had the right to live his life according to the interior lights given to him.
One common idea about medieval Europe was that everyone were firm believers in religion. If you were a Christian (or a member of the smaller Jewish and Muslim communities), then you accepted your faith without question. However, a closer look at the evidence reveals that people in the Middle Ages did have doubts about religion, and even espoused views that we might call atheism.
One of the most important studies in this area was published in 1988: “Religious faith and doubt in late medieval Spain: Soria, circa 1450–1500,” by John Edwards made use of records from the Spanish Inquisition to better understand some of the popular views on Christianity.
There is a universal dimension to some of the accusations in these statements. They included generalized attacks on Christianity or attacks on specific aspects of the church’s teaching; blasphemy, which moved easily into humour and obscenity; materialistic views about this life and scepticism about an afterlife; a belief in the validity of other religions and the possibility of achieving salvation by following them; and, finally, the use of magic.
Among the most vivid descriptions recorded by the Inquisitors are accounts of blasphemy, many which took place in taverns or during games of chance. For example, in 1494, while playing a game of bowls, Bernaldino Pajarillo angrily cried out, “I reject the whore of a God!”. Six years later a surgeon, Master Bernal, urged on his slowing bowl with the cry, “Get there! Get there! May Jesus Christ never flourish!”. Meanwhile in 1487 Rodrigo, a draper, was said to have shouted while playing pelota, “I don’t believe in God, buggering St. John!”. Another gambler, Lope de Vallejera, who was once a page to the Countess of Denia, was said to have cried out, “I reject the @#&@#@# Jewish whore of a God!”
While shouting blasphemy in anger might be taken for granted, the Inquisitors were also told about people who made specific statements attacking their own Christian faith. Edwards writes:
A cleric, Diego Mexias, said in Aranda about 1485 “that there is nothing except being born and dying, and having a nice girlfriend (gentil amiga) and plenty to eat”, and that there were no such things as heaven and hell. The late Pedro Gomez el Chamorro, of Coruna del Conde, expressed similar “materialistic” views in 1500, “warming himself by the fire, annoyed and and fed up with the weather there was and the cold”. His complaints about the weather led him to conclude, “I vow to God, there is no soul”.
… Pedro Moreno, a chaplain, seems to have tired of the conversation of a group who were talking, in conventional terms, about the activities and attributes of the saints. It was said that, “St. Michael held the balance, and St. Bartholomew held the devils in chains and St. Peter had the keys of heaven”, to which the cleric replied, “Yes, in his jock-strap”, and, as the female witness solemnly recounts, “some of those who were there reproached him”
One of the most interesting comments comes from Diego de Barrionuevo, who was accused of saying in 1494, “I swear to God that this hell and paradise is nothing more than a way of frightening us, like people saying to children, ‘Avati coco‘ [‘The bogeyman will get you’]”
The records included accusations against eight men and one woman over their beliefs that Christianity was not the only path to salvation. The woman for example, was a peasant farmer called Juana Perez, who said in about 1488 that “the good Jew would be saved, and the good Moor, in his law, and why else had God made them?”
Medieval evidence thus seems to support the general principle that religious doubt is an intrinsic part of faith. Therefore, even if Febvre was right to argue that “atheism”, in any modern sense, was not an option in the sixteenth century or earlier, it does appear none the less that there was indeed genuine religious scepticism in late medieval and early modern Europe. The question which remains, though, is where and how such an attitude originated. The striking similarity of material from such widely differing regions and periods raises important issues concerning the interpretation of “popular” religion and its relationship to the religion of “elites”.