Just saw the Thracian (sp?) chariot on /r/pics and was curious.
Morally, or legally?
In the UK, Victorian fears of grave robbery (to supply cadavers for medical school dissections) led to the creation of a law which requires a permit to excavate any body, and archaeologists today have to apply for the permit even when excavating prehistoric burials. But each country has its own regulations, and I can't speak for conditions outside the UK.
Even very recent bodies can be subject to archaeological research, the most notable and macabre examples being the excavation of mass graves (such as in Guatemala and the Balkans). Where there is a reasonable possibility that a person has a descendant, the ethics rests heavily on their opinion--if a descendant wants a twenty year corpse exhumed, it is ethical, if they don't want a five hundred year corpse exhumed, it is unethical (although this can get complicated).
Beyond that, what matters is the reasoning and manner of an excavation, that is, it is only ethical archaeology if it is conducted in a manner that guarantees both the public and scholarly interest. What makes George Bass and archaeologist and Odyssey Marine two-bit thieves is not the age of the ship they excavate, but they way they do it and their motivation for doing so.
There was a pretty long thread on this very subject about a year ago. Here's the link.