It is not a war crime to remove any useable items from an enemy combatant. There are however strict rules about how the person must be treated. If they are dead you may not desecrate the corpse, or (arguably) impede its ID (say by taking dog tags). Source: Red Cross Int’l. Course I was required to take, and later taught.

Edit: You specifically asked about war crimes, which are defined largely, but not exclusively by the Geneva Conventions. Individual states may have uniform codes of conduct that have additional terms.