Your question only really makes sense to me if I assume that you're talking about Europe (slash the West in general) specifically, so I hope you don't mind if I focus there. There have been many, many cultures around the world where women did not wear floor-length gowns.

Between the Middle Ages and, say, the 1920s in the West, long gowns were common. But we have to explore what "floor-length" means. If your question is literally "were dresses that literally touched the floor all around the body common", then no, they weren't. Are you actually seeing floor-length skirts in historical dramas? Is a skirt that comes down to the ankle or the top of the foot floor-length? This might seem like hair-splitting, but it's relevant - because gowns that were actually floor-length are fairly uncommon.

The main reason is class. Fashion always changes subtly by class because a major part of fashion itself is class differentiation: the wealthy have historically used both expensive materials and the newest styles to show their wealth. A wealthy woman can also manage to go about her daily life in less practical clothing, whether that means that its cut prevents the arms from fully rising or the hem is trained, while the more physical work a woman needs to do, the more allowances she needs from her clothing.

A good example of the clothing of different classes at the earlier end of your timeframe is Les Très Riches Heures of the Duc de Berry from about 1415. The page for April depicts a noble wedding, in which both men and women wear vibrantly-colored clothing that trails on the ground behind them and pools at their feet in front of them. Their sleeves are as long as their skirts, cut to flow out flaringly. June, on the other hand, depicts peasants laboring in the fields. The men are wearing breechcloths, shirts, and nothing else, baring their legs; the women are wearing gowns that are pulled up through their belts (hidden by the gown puffing out over them) to come to mid-calf or just above the ankle. The women's sleeves are also very short, with their chemises underneath being revealed, and the clothing is dyed in lighter/more earth-tone colors, apart from the one bold blue gown.

Moving ahead several centuries, we can see similar differences between a lady painted by Arthur Devis and "La Pourvoieuse" or the woman in "The Enraged Musician". The woman identified as a lady wears a fashionable robe à la française/sacque in a fashionable pinky-peachy silk over a wide hooped petticoat, and the hem comes quite close to the ground, although it doesn't actually touch. The pourvoieuse, on the other hand, is wearing a loose bedgown over several petticoats, which give her a slightly belled silhouette, and the outermost petticoat is cut to end above her ankle, where the raw edge is bound with a tape. The woman in the satirical print is wearing a more fitted gown, but her skirts/petticoats likewise also end above the ankle. A skirt this length is much less likely to be stepped on while walking or going up stairs.

In both periods and those before, between, and after, there were many more people dressing like the latter examples here than the former, which is why I'm saying that no, floor-length gowns were not common. However, from another perspective, wealthy/noble/royal women throughout the same time frame did normally wear gowns that went to the floor, or nearly so, so it also was common. There are exceptions - the late 1810s through early 1830s, for instance, had a fashionable skirt length that was a little higher - but by and large, yes. There were even periods, such as 1785-1810 or 1867-1890, where a train that quite definitely dragged on the ground was in fashion. However, the affluent women who were dressing like this protected their clothing in a couple of ways.

One is by having a facing or a braid under the bottom of the skirt that could be cleaned and/or replaced as needed. Many late 19th century gowns can still be found today with "dust ruffles" - industrially made lengths of ruffled fabric that could be cut to size as needed - sewn to the underside of the train. It was also quite common for women to simply take a handful of the back of the skirt to hold up the train as needed.

However, a major way they dealt with it was to just not wear these gowns to do a lot of walking in dirty conditions. They were indoors a lot: they might go out for a promenade in the garden or to go shopping, but the majority of their time was spent inside buildings or carriages (like modern-day people, really). Particularly toward the end of the period you're talking about, wealthy women were likely to have specialized clothing for outdoor activities and traveling, made with slightly shorter skirts and no trains. And, of course, they had servants. If you are not in charge of dealing with the dirt on your hem, it is really not a big deal to you to occasionally trail your skirt in the mud.