I like using triggers for validation important for maintaining data integrity.

Example: let's say you have a parent table P whose rows are soft deleted (update P set _deleted=1 where id=?) and a child table C (foreign key on P.id) On delete cascade isn't gonna work here obviously. So I use a trigger to emulate on delete cascade.

Also, I've seen triggers to cancel transactions raise abort(..) if they violate some property that can't be retrofitted into a proper db constraint due to team politics at a previous workplace.