I would say that the whole "looting" issue depends on the character's background and alignment. There are plenty of instances in fiction where a character takes a fallen companion's equipment:
In the the Fellowship of the Ring (strictly speaking, the movie), Isildur takes up his father's sword and destroys Sauron. This is an instance where the item is a family heirloom. The sword is broken, reforged and taken by Aragorn (not stated in the movie, but it's in the book).
Also, Isildur takes the Ring from Sauron (his vanquished foe).
After his death, Boromir is floated out into the river with his shield and sword, but Aragorn keeps his Gondor-embroidered bracers, possibly a token of remembrance.
In Star Wars, Obi-Wan Kenobi (presumably in Episode III) defeats Anakin Skywalker and takes his lightsaber, only to later give it to Luke in Episode IV.
I think Lawful or Good characters might have moral qualms about just looting the bodies, especially if they are Lawful or Good Fighters, Clerics or Paladins. Neutral or Chaotic characters might do it out of a perceived necessity or utility. Evil characters would probably do it just to spite the fallen foe.
Like the previous poster mentioned in modern warfare, utilizing a fallen companion's equipment is not considered looting, of course the weaponry and equipment are property of the service, not of the character. You probably wouldn't see a soldier swiping the fallen comrade's credit cards, crucifix or other personal items.
I guess it really depends on alignment, class and whether equipment in your campaign really has sentimental value or if it is the proverbial "+1 longsword of the week.)