For most of Dalek history, there was no Emperor, but there was a Supreme, or a Prime, but let's pretend those are all the same thing to make things simpler. There still have been plenty of Daleks who were independent of whoever the leader was.
The Cult of Skaro were specifically created to act independently ("Doomsday"), and there have been less extreme experiments of that kind in the past.
There have also been times when there was no Emperor, Supreme, or Prime, and any Daleks alive at those times were independent. That tends to make them nervous, unhappy, and frightened, as you can see from "Dalek", "Jubilee" (audio story), "Victory of the Daleks", etc.
And finally, there have been multiple civil wars. Most famously, in "Remembrance of the Daleks", the Renegade Daleks were independent of Davros, Creator and Emperor of the Daleks. Of course they just followed the Dalek Supreme instead. But in the early planning stages of each civil war, there were obviously some Daleks who were ready to rebel but didn't yet know who to obey instead. (We see a tiny bit of this in "War of the Daleks" (novel), although most of what we see in that book is pretty ridiculous.)