How to open jammed shut off valve
That hex nut is the packing nut, which you may need to loosen in order to actually turn the valve off with the gear-looking part of it (the valve stem), and then tighten the hex nut back down or it'll leak from there now too. 

Seeing as you don't have a handle anymore anyway, and that it's being difficult, replacement of the entire valve (with a quarter turn valve) should be considered.

If you can't get the valve stem to turn, and you can't get the packing nut to loosen enough to do so with an adjustable wrench, then it's about time for a new valve, so go ahead and try it. Use a quick, snapping motion to break it lose. Do it too slow, even with a well fitted wrench, and it might deform anyway. 

Turning off your main valve comes with its own set of problems, so I'll leave that choice up to you, but before you begin, you should at least know where it is.

If you're really trying to not have to replace the valve, this is the procedure you'll have to use to open or close it in the future: 


Loosen packing nut.
Turn valve.
Re-tighten packing nut.


Use a quick, almost snapping motion to break it lose with an adjustable wrench. Use a pipe wrench with a rag wrapped over the valve body to 'back it up' or you risk unthreading the entire valve from the wall. Put the pipe wrench where the tee is, to stabilize the valve, and apply torque in the opposite direction of your other wrench.

Sometimes you have to tighten threaded connections a little bit, that you're trying to take lose.