welcome to the Jeep scene. There's a lot of good information here on the forums and plenty of helpful people. One thing we do request is that you do a little research before posting just to make sure the info isn't already out there. At the top of the forum are some stickies which handle some of the more common questions like yours.
Just for reference, any JK can run 32s with a stock suspension without an issue. Rubicon models come with 32s. As far as how wide can you got, you can check the tire size on a Rubicon as a good starting point and can even check the tire manufacturer's website on what size wheel the tire will fit on. If you go too wide you do run a risk of rubbing when at full turn. Hope this helps and don't forget to wave.
'09 X Unlimited, 4WD, auto, half-doors, soft-top
RC 2.5" Series II BB, JKS Quick Discos, JKS adjustable front track bar
15x8 Unique 297 (Soft 8), Goodyear MTR/Kevlar 35x12.50R15
5.13 gears, ARB front locker, Currie front shafts
Bushwacker flat flares, Rubicon rails with steps added