The rule of thumb I use for all terrain tires and MT tires is what I call the 4" rule. As long as the tread width is within 4 inches of the rim width, then you are good. When you start going with low profile tires, then the difference can not be as great. I am running 37x12.5's on an 8" wide rim. They fit on there fine and keep the rim out of the way during 4x4ing.
Just keep in mind that when using a wider rim, it can lead to clearance issues as the backspacing is remaining constant, so, all the additional width is going to the outside edge which will lead to the tire touching the back of the front wheel wells sooner. For example, with a 4" lift, you can fit 315/75R16's (aka, 35x12.5's) on an 8" rim, but if you were to use a 9" wide rim or wider with the same backspacing, you will have rubbing issues. So, it is a balance between what you want and what you have clearance for.