As part of the TU14 update for Minecraft Xbox 360 Edition trip wires & trapped chests were added and YouTuber Br3th3n has made a useful guide explaining how they can be used to trap your friends.
To set up a trip wire hook all you need is a single iron ignot, a stick, and a wooden plank. Once you've made the hooks for the wire you can place them on blocks up to 40 blocks apart and then you simply need to place your string between them – you'll need one piece of string for each block.
This done, you can then place a dispenser for arrows, TNT. or spawn eggs etc. Disabling a trip wire is allow pretty straightforward; you just need to go to the wire and snip it with your shears.
If you're looking to make a trapped chest you'll need a trip wire hook and a chest. By placing a redstone torch under the block with the chest and link it with redstone to another nearby block attached to a redtone torch which is in turn connected to TNT, a fireball, spawn egg, or arrow dispenser.
So when your friends come to steal from chest opening it will set off the TNT or whatever you used, blowing up them and the chest. A piston can also be used so that the floor collapses under your friend when they open the chest spewing them into a pit of lava or something like that.
You can check out the video below; even though it's PC footage, the same principals apply to the Xbox 360 version of the game.