Many things. Never a weapon, but other things such as shields, Holy/unholy/balance books. Defenders (rune defender adamantite defender etc.)
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you can dum noobs you have to do a quest first -.-
If you have a weapon in your inventory, click on it to wield it. This will un-wield any other weapon you have in your weapon slot.
It saves a spot when smithing because you can wield it.
A shield or a prayer book. sheild, book and 2h sword
In the current game you cannot dual wield. However it was confirmed in one of the behind the scenes video's that dual wielding would be introduced as part of the evolution of combat update.