My time to shine! I'm assuming we are talking about English?

There's a number of things you could say. However, swearing and taboo language in the middle ages was very different from how it is now. You have to understand what was considered truly profane.

Think about the words swear and curse. That's important. Words we consider profane, like fuck, shit, ass, etc, weren't really that bad. Most of our swearing comes from bodily functions. But privacy wasn't really a thing for a Middle Ages peasant. Your parents probably made love in a bed right across from yours in an open room, and it was considered normal for people to spit at the table. These things weren't taboo. Ants might be called "pisse-mires" a flying bird could be a "wind-fucker." Perhaps while fishing, you caught a "shite-row". Streets where people went to the bathroom in alleyways could be called "Shitwell Way." Prostitutes lived on "Gropecuntelane*", which doesn't take a genius to figure out. Gropecuntelane is still a street name in London iirc. The truly taboo thing was religions swearing. The swearing of oaths was a very important aspect of society. I can't even overstate it. Swearing, as in swearing to be truthful in court, was the basis of a number of social systems. The court system would fall apart if people swore false oaths. And false oaths were a big no no. You could back up an oath by making it religious, like swearing by the cross, or making an oath over the grave of a Saint. One of the reasons William the Conqueror strolled into England was, on paper at least, because the previous King of England had sworn over the bones of a saint to give the crown to William instead of another guy.

Backing up your oaths with religious intent had power. If you swore by a particular part of Jesus' body for example, it was believed to have a physical affect on Jesus up in heaven. So if you said "I swear on the stigmata, I didn’t steal your chicken." And if you did steal the chicken, then Jesus would start feeling terrible pain since your false oath was affecting him. A really popular one was "God's Bones." So if you stubbed your toe on the door and yelled "By God's Bones, that hurt!" Then you were basically giving God himself a kick in the shins.

 Cursing people was also a no no. Again, think about the words swear and curse. We've covered swearing, but cursing was also very, very taboo. While relatively mild today, saying "God damn it" or "Damn you!" Was pretty serious, as you were asking God to send a person to hell for all eternity. 

There were of course, other words of I'll intent, or at least rude ones. "Sard" carries the same impolite connotations and meaning as the modern "fuck" if used in a sexual sense. A translation of the Bible has a commandment about not "sarding another man's wif."

I highly recommend Melissa Mohr's Holy Sht!: A history of swearing* for more info. It was also my major source, as well as some previous knowledge.

Sources: Holy Sht: A Brief History of Swearing*, Melissa Mohr, Oxford University Press.