With the weekly reset, we've confirmed that rare mobs grant reputation each week they're defeated!
This is a change from the beta, in which they awarded reputation daily per account, though that was clearly not the case over the course of the last week during Early Access. As is stands, each rare mob awards 150 reputation depending on the zone it is in (or 50 notoriety for each of the three pacts in Azj-Kahet).
Defeating a unique rare will drop 150 Reputation for the zone it is in!
There are a variety of AddOns such as HandyNotes and RareScanner that can be used to aid players in hunting down all of these unique rares.