Like Dan said, it depends on your state and location.
In Indiana, state law reads that the trash is owned by the person throwing it out or by the garbage company that is picking it up.
I don't dumpster dive, but from what I've heard, the police, around here, are taking issue with many of those who are caught diving, but again, this is a YMMV.
I have a friend that works at a local business. They would have cared less about people diving, but the scrappers found it, and were leaving unbelievable messes. They were emptying the entire dumpster, and cutting bags open on the ground.