These are not concrete examples and all insurers differ, but some reasons why an insurer might not pay out include:
In certain circumstances it will not cover extreme sports or expeditions; don't book a trek to the top of Mount Everest and expect standard insurance to pay out in the event of a disaster
Loss of items or injury through negligence such as alcohol
Ignoring FCO (Foreign & Commonwealth Office) advice
Full cost of valuables (see below)
Failure to report crime within a certain time frame
Lateness (e.g. missed flights)