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.