I understand that the plain Native Americans used tipis and the people of the Eurasian Steppe used yurts, but what dwellings did other nomadic people use?
Very common over much of the world were structures with a stick frame, using either straight sticks or bent sticks, or a combination of the two, covered with brush or bark or leaves. The materials are gathered locally, and the structure abandoned when the occupants move. If they return to the same site, the frame might be re-used. This type of structure is common for nomads who walk, since none of the structure needs to be carried from camp to camp. They provide shelter from sun, wind, and rain. Sometimes, living trees are used as part of the structure (as a post), or the structure is built against a large rock.
Some examples:
Australia: https://commons.wikimedia.org/wiki/File:Native_Encampment_by_Skinner_Prout,from_Australia(1876,_vol_II).jpg
Africa: https://commons.wikimedia.org/wiki/File:Living_on_the_rainforest.jpg
North America: https://commons.wikimedia.org/wiki/File:Nu-nu-shi-unt,_the_dreamer.jpg
North America: https://commons.wikimedia.org/wiki/File:Apache_Wickiup,_Edward_Curtis,_1903.jpg
Where hides are available, and transport to move the hides from camp to camp is available, a similar frame can be covered with hides. You already mentioned one classic example, the tipi. Sometimes, the frame is also moved from camp to camp, and sometimes the frame is abandoned. Sometimes, parts of the frame for which it might be difficult to find suitable pieces of wood are moved, but most of the frame is abandoned.
Northern Europe: https://commons.wikimedia.org/wiki/File:Saami_Family_1900.jpg
Northern Europe: https://commons.wikimedia.org/wiki/File:Sami-tent.jpg
Sometimes, if the site will be revisited, the base might include rocks or earth:
Other choices for covering include felt and woven cloth, both used in Asia. Especially in areas lacking trees, the entire frame is moved from camp to camp. You have already mentioned the yurt/ger. Where the whole structure is dismantled and moved, often more use is made of ropes rather than sticks - that is, the stucture is a tent with tent poles and ropes, and a cover.
Tibet: https://en.wikipedia.org/wiki/File:Old_nomad_tenttibet.jpg
Tibet: https://commons.wikimedia.org/wiki/File:Nomads_near_Namtso.jpg
If sufficient animal traction is available, and the terrain suits, the entire structure can be mounted on a wagon:
The dwelling can also be built as a permanent superstructure on a wagon:
We can also note that some of the users of the modern motorised or motor-vehicle pulled versions (mobile homes, RVs, caravans) are nomadic.
Another class of mobile dwellings are boats. While most boat users have permanent dwellings on land, some live permanently on their boats. Boat-dwellers can either remain in the same area, or they can be nomadic.
Another local material that is used is snow:
One interesting building material that has fallen out of fashion and availability is mammoth bones:
https://www.reddit.com/r/ArtefactPorn/comments/b1elhm/hut_made_of_mammoth_bones_cromagnon_mezhirich/
Reconstruction: https://i.pinimg.com/originals/40/a9/c9/40a9c9a8e60832ede142b2b895df5d3c.png
While we don't know for sure whether the occupants were nomads, it is likely that they were, following mammoth herds.
