I would imagine that there's a lot of ground covered by "tomb robbing."
At the high end of the spectrum, I think you'd find Tom Bombadil of the Lord of the Rings. He breaks into the barrow wight's tomb, kills the inhabitant, takes one piece of treasure, and gives others to his allies then leaves the rest for whoever finds it.
Technically, it could be described as tomb robbing but it's quite clearly presented as rescuing those weaker than himself from an evil being and then laying that evil to rest forever. There's also the matter of the wight not being the original inhabitant of the tomb but rather an evil spirit that crept into the tombs after the fall of Anuminas.
Then there are characters like Indiana Jones and Lara Croft. Clearly, they're not in the same category as Tom Bombadil, but their interest is not entirely mercenary. Finding enlightenment (or at least interesting artifacts or the truth of ancient legends) is at least as important as gold.
Then there the tomb robbers who kick the body aside and take the grave goods to melt down for gold.
I'd guess that most DMs will approve of Tom Bombadil style interactions with tombs for exalted characters but that Indiana Jones/Lara Croft style interactions are probably borderline.
In fantasy, there's another category that's probably fine too. Taking the artifact that can stop the hordes of evil. Or taking the weapon that is near at hand to stop the immediate evil. I doubt that any DM would have a problem with an exalted warrior fighting in the Lonely Mountain and realizing that his sword cannot pierce the flesh of his attackers taking Orcrist from Thorin's tomb to rout them. (Whether or not he would need to put it back when he finished would be another question).