It seems whenever they show up, it's either just Carol, the universe is coming to an end, or they're under attack. The closest I remember them doing their job is that one time one of them attacked Kyle and Soranik so they would get over their relationship troubles.
The Green Lanterns are cops, the Red Lanterns are the Punishers, Sinestro Corps are the Batmen, Blue Lanterns are the spiritual leaders, Star Sapphires are... what?