DIM is a Chrome extension that lets you move stuff between characters and the vault or directly between characters. It lets you equip and dequip gear, too. And it lets you see what you have at the postmaster, though you can't access it (yet.)
I had my Titan out on a mission and realized I forgot to take my stack of 3oC off of my Hunter. Rather than having to abandon the mission, switch to the Hunter, travel to the tower, move the 3oC to the vault, switch back to the Titan, travel to the tower, retrieve the 3oC from the vault, travel back to orbit, restart the mission... all I have to do is open up DIM, select the 3oC stack in my Hunter's inventory, click "Store <Titan emblem>" and the stack magically appears in my Titan's inventory. All in real time as the mission is in progress. It's fucking glorious and fixes one of Destiny's biggest problems.
The only non-quest reasons I need to go back to the tower now are for decryption and postmaster.