Examples are areas where a study takes advantage of a sudden, unexpected event. For example, there have been studies about human memory related to unexpected tragedies. There was an idea that lots of Americans remembered exactly where they were when they found out that President Kennedy was shot. After the Challenger disaster, a study was done where they asked people where they were when they found out, and then asked them different amounts of time later (e.g. a year, 5 years and then ten years out), and they found that despite people being very certain of their memories, many people had recollections which changed drastically in the intervening time. Similar studies were done later for the Columbia disaster and 9/11. See summary [here], and 10 year followup to 9/11 [here]. These would be extremely hard to preregister without substantial ethical problems; I suspect that most journals and the public would frown on psychologists deliberately causing large-scale national catastrophes in order to preregister their studies.
The World Trade Center attack also provides also an example from another field: Right after 9/11 airplanes were grounded throughout the US. Multiple studies used this as an opportunity to study the impact of airplanes on the atmosphere. See here.
Editorial remark: The set of studies where preregistration is not feasible is a very tiny fraction of all studies, and the fact that such studies do exist should not in general be taken as an argument against broad requirements for preregistration.