Depends on the building first, then on tradition.
Tradition had just pressed ground flooring, specially in pressed adobe houses. Then planks - hard wood if possible (oak, specially black oak, could last forever), but that may have been too expensive so simple pine with a good few coats of paint would last just as long. In taverns, it wasn't painted, as any paint would soon crack after so much foot traffic and furniture dragging. So they used raw wood but oiled it regularly, using petroleum or crude, as it would soak the dust. This practice also held for many shops into late seventies.
There was always the parket, i.e. hardwood cut into grooved slats sized 5x25x2 cm, which would be arranged tightly into zigzag pattern, then planed and finally lacquered in several layers. The lacquer would hold for many years. The downside of this was that it was also used for gyms, where the lacquer was unapplicable - too slippery - so the wood was left bare. Any leak in the roof would make one section wet, the slats would grow in volume and the whole section would buckle up, which was even dangerous. Still, this kind of hardwood floor is always popular, requires only relacquering every 20 years or so, lasts forever.
The other traditional flooring was stone slates, cut into squares of 20x20 (or 25 or 15) centimeters, usually about 20-30mm thick. They weren't necessarily cut stone, frequently they were grains cemented into this shape. The top surface would be smoothed out by grinding. The other variant of this was pouring whole floors of such ground stone and polishing the top. This would then be waxed. Such floors were popular in institutional buildings - city halls, barracks, schools, hospitals.
They were probably hard to make so they were gradually replaced with lynoleum first, then concrete floors covered with vinyl-asbest tiles. These lasted rather long if glued (with heated tar) properly, and were rather popular for supermarkets, some parts of department stores and cheaper restaurants. Somewhere with the lynoleum was the so-called "warm floor", which was actually a very thin variant of lynoleum, padded with some felt on the underside. It was cheap, looked well while new, and didn't last. It would soon get its corners bent, torn in places and started looking ugly. Seen them in small offices like janitor's, ticketing etc, wherever people were supposed to spend long hours or night shift in a badly insulated cabin, to at least give them some insulation for their feet.
In the seventies several kinds of synthetic wall-to-wall carpets were developed. These weren't stretched with knee kickers etc like they do in the US, they weren't elastic that way. Instead, they were glued to the concrete slab, which still holds in places where these weren't replaced. These were popular in apartments, tourist agencies (even on walls), hotel lobbies etc.
Nowadays the most popular thing is laminate. It's imitation hardwood, with the top surface looking like wood and pretty much feels like lacquered wood, but it's actually plastic. The inner layers are probably wood particles, plastic and glue. They come in slabs of decent size (2, 3 or 4 m by 0,5 or so) so they are quick to lay. Most new or remodeled apartments use this for rooms.
The next popular thing are the ceramic tiles, or in the more posh and expensive variant, marble. The tiles used to be 15x15 or 10x20; nowadays the 33x33 is the more popular format. The reason for larger tiles is the speed of laying and the general ability of masons to pour flat surfaces, which is much better than it used to be. Tiles are pretty much mandatory for all rooms in houses with in-floor heating, as it doesn't make sense to cover your heating body with insulators, i.e. rugs. And of course, most of kitchens and bathrooms are tiled with ceramics; there may be a few left with vinyl asbest.
Rugs were always popular and there was a big industry of those. Traditionally, they were something made at home, of rough and brightly colored wool, with fringes on shorter edges. These were gradually replaced with industrial rugs, which were mostly high quality, good (and often imaginative) design. Their only downside was that they were always bought smaller than they should be, so no matter how you sit, the rear legs of your chair would get on and off the rug's edge, and the edges would fold.