At what altitude(s) do dogfights typically occur? How has this changed from World War I up to now?
At what altitude(s) do dogfights typically occur?
All of them.
Throughout history dogfights have generally started at one of the aircraft's "best altitude", which depends on the aircraft, and then descended as the pilot's trade altitude for airspeed.
Altitude disparity can be so great that one or the other will simply not engage, or do so at a serious penalty if they are forced to. This occurred during the Falklands when the Argentinian aircraft had much more performance than the UK's Harriers, but only at higher altitudes. The Harriers simply refused to fight them, so if the Argentines wanted to get to the ships they had to fly down where the Harriers had the advantage. The same occurred during WWII when US B-17's flew at altitudes where German fighters were struggling, allowing the escorting P-51's to chew them up.
It is not uncommon for extended dogfights to end with troops on the ground shooting down some of the aircraft, as was the case with the Red Baron (or so the Australians will claim).
WWI dogfights would generally be between 5-15000 ft. Aircraft could patrol up to 20,000 ft (yes, without oxygen). The Camel had a service ceiling of 19000 ft, the SPAD XIII almost 22,000 ft.
In WWII, generally between 20-35000 ft over W Europe, under 20000 ft over Russia and in the far east. Bomber escorts in W Europe started out hanging with the bomber formations just above at perhaps 25-27000 ft, but later when they were sent to range on ahead, they would patrol at 30-35000. The FW190-A8 had a service ceiling of a bit over 37000 ft, and the Mustang just over 40, but at service ceiling there is almost no spare energy available for maneuvering so you couldn't actually fight at that altitude for any length of time.
In both WW's, once started the fighting aircraft would get lower and lower as they consumed energy, that would normally be available for climbing, in maneuvering for advantage, and in long fights they would end up near the ground.
An interesting aspect of high altitude combat in unpressurized airplanes was the risk of getting the bends from extended exposure to the low atmospheric pressure above 25000.
Today, I would say 20-50000 ft.