Not only do these three words sound practically the same, their meanings are so similar that people often confuse them.
Incidence means the degree or extent of the occurrence of some phenomenon.
The incidence of dry holes has decreased significantly since the advent of 3D seismic.
Incidents, the plural of “incident,” means “occurrences.”
Lost time incidents have decreased for company personnel, but not for contractors.
Instances are examples, illustrations, or realizations.
After the merger, the IT department found itself supporting six separate instances of SAP.
As noted by Paul Brians in his book Common Errors in English Usage, “Incidents can be used as instances only if someone is using them as examples.”