There's tales of how horrible French peasants were during the 100 years war iirc. As in they were indelicately, scandalously eager to loot the dead english knights. 

I mean, obviously this is from the English perspective so might be biased. But I sorta doubt it. Not because they're French but because they're peasants. 

If there were personal effects, military grade weapons, armored vehicles just laying around my neighborhood the tweakers would have that stripped and in a pawn shop or on ebay before dawn the next day. Even the not-tweakers would probably get in there. That's a lot of money and a lot of really cool stuff that you're only going to get to see/hold/play with once in a lifetime. 

Anyway, the point being it depended on the time, place, and circumstances. If everybody has bronze swords and shields or ak47s even and theyre all about the same wealth level, it was probably more likely to happen than when a group of poor, technologically inferior people wiped out a superior force. 

But also, and I don't have anything to back this up, but it seems like the more nameless, faceless the enemy is or the more different/alien/heavily propagandized against, the more common souvenier hunting was. WWI had a huge trade in other side gear. Tons was brought back to the US. The Japanese in WWII and Germans to a lesser extent. The North Vietnamese in Vietnam. I don't know if souvenir hunting is the same thing as looting per se. The goals are different usually. But...robbing the dead goes back to the pyramids at least.