Non-native species?

This topic is being discussed in another thread, so I figured I would try to clear up some confusion in my own mind about the term "non-native".

What exactly defines an organism as being "non-native"? Physical boundaries being crossed intentionally or accidentally? Human hands must be involved? Or can any other organism that introduces another organism to some place it has never lived before play too? Is there some time limit as to when any "natural" form (whatever that might be) of migration of a species has to have already taken place before the door that considers them as being "native" is shut?

Seriously, this has always puzzled me. Sort of like the designation of "locality" animals. Are there any definitions that are not just arbitrary in nature, and push come to shove, a definition made up by a species that is itself non-native in most of the habitat it is now found in?