When should the IGNORE_DUP_KEY option be used on an index?
It's definitely an atypical setting to enable for an index. I don't think you're going to find many people who jump up and talk about using it.
Of course, there are a couple helpful posts on the subject by Paul White:

IGNORE_DUP_KEY slower on clustered indexes
A creative use of IGNORE_DUP_KEY

If your concern is around upsert patterns (or something similar), this article by Michael Swart is really informative:

SQL Server UPSERT Patterns and Antipatterns