No 16th-century houses contained what you or I might recognize as "bathrooms" - places to get yourself cleaned up as well as cleaned out (sorry). But unless you were royalty (and sometimes not even then), cleanliness wasn't exactly a top priority for people. In fact, most people were convinced that bathing was actually bad for one's health, in that it opened the pores and thus allowed all the nasty stuff floating in the air to gain entry into one's body. You've heard the term "the great unwashed?" Commoners who washed their hands and faces on a fairly regular basis, but bathed once or twice a year, felt pretty righteous about their personal hygiene. For the most part, royals bathed more frequently, but they didn't need a special room for that purpose. Anything that kings or queens, or other very rich people, wanted while anywhere in their homes, including bathtubs, turned out to be amazingly portable. But some royals didn't take advantage of this perk. James VI of Scotland was notorious for his filth, and for not changing his clothes for months on end.
The question arises: if most people hardly ever washed, didn't they stink? Duh. Of course they did. Everyone in the Middle Ages was just used to it. Wealthy people sometimes doused themselves in perfumes to try to mask their natural odors, but it's probably debatable how much of an improvement that represented. You know the word "nosegay," which nowadays just denotes a small bouquet of flowers? Back in the day, members of the upper classes would carry nosegays around with them wherever they went so they could bury their noses in them when the ambient body odors got too overwhelming. That was how they kept their nose gay (in the sense of happy). Get it?
But no doubt there were those who, through no fault of their own, just stank more than others. This seems to have been the case with poor Anne of Cleves. Henry VIII of England chose her as Wife #4 based just on a photograph, and was terribly dismayed when she arrived from Germany to meet him in person. He could reportedly never bring himself to consummate their marriage, which ended in divorce six months later. Luckily for her, he apparently didn't consider body odor, no matter how extreme, to be a capital offense, and she spent the rest of her life in comfort, choosing never to return from England to Germany.
Unlike bathing, excretion - the other reason to have bathrooms - is unavoidable, and so some kind of arrangements had to be made. Actually, on the subject of excretion, the poorest classes had the biggest bathrooms, otherwise known as the great outdoors. But this convenience did not usually equate to comfort, especially in the winter. Nonetheless, indoor bathrooms wouldn't become commonplace in Europe for several hundred more years. (I'm focusing on Europe in this post out of necessity. I could find very little information about toilet habits in other cultures.)
For centuries preceding the 16th, middle-class people had used chamber pots in their homes so they wouldn't have to go outside to relieve themselves. They would either just crouch directly over the pots, or (in a slightly fancier version) sit on a piece of furniture known as a close stool - designed to look like an ordinary chair, but with a top seat that lifted up to reveal a hole in the middle of a second seat, positioned over a concealed chamber pot. So classy.
But either way, the chamber pots had to be frequently emptied by servants, and where were the contents dumped? Directly into the streets and gutters, of course! I'll spare you further details about this practice, other than to say that by the 1400s, walking in the streets of any European city was a very hazardous and noxious exercise, to say the least.
To address this increasingly horrifying public health problem, in the 16th century city home-owners began hiring workmen to dig cesspools near their houses so that at least the waste could be stored away from the streets. Chamber pots began to be replaced by crude indoor toilets known as jakes or garderobes (basically a slab of wood with a hole in the middle, positioned over a pit), which were connected to the cesspools by a series of pipes.
I regret to inform you, though, that in castles the pipes frequently emptied directly into the surrounding moats. At least the cesspools got shoveled out from time to time. The moats, not so much.
Some garderobes didn't bother with pipes. They simply jutted out from the exterior side of a wall, like so:
Um, that's a gaping hole on the bottom. Yep. Exactly. Look out below.
Of course, the royals had their close stools brought to them whenever and wherever they felt like, and they had servants wipe their butts for them with sponges attached to the end of a stick. Do you think I'm lying about all this? Go look it up! "Groom of the King's Close Stool" was a coveted position at court, involving carrying the extremely fancy stool around all day for whenever the need arose, and then standing by while it was being used.
You might think this job was considered demeaning. Shows how much you know about monarchies! No, only well-born gentlemen got the assignment of the Groom of the Stool. Seems that it was the proximity to the monarch, not the actual tasks performed, that mattered.
And if all of this brings you a newfound appreciation of indoor plumbing, my work here is done.