Well, LJRubiconGuy, here is what I take with me, and the conditions that I off road in. Let's start with where I go Off Road. I live in the Pacific Northwest. My territory is from the east side of the Cascades to the beaches on the Pacific. Geologically speaking the terrain is steep to very steep. There are literally thousands of miles of un-maintained blacktop, gravel and dirt roads within that area. BLM, Forest Service, and the State Department of Forestry lands make up more than half the area in the region. Add in the private timber lands and I would guess that 80% of the area is forested to one degree or another. The coast range is covered by triple canopy temperate rain forest. The Cascades are covered in climax evergreen forests. With that said, the trail conditions are close. More than 90% of the time the trails are actually narrower than the Jeep and much steeper than anything you will find with normal travel on normal roads. Dry and dusty to wet and muddy to covered in snow. The Wrangler is way more capable of navigating these conditions than anything else I've ever owned. The big BUT is, you need to use good judgement. Don't ask yourself "Can I?", ask yourself "Should I?".
With all of that being said, here is a list, from memory, of what i throw in the rig each and every time I head out. It's been pretty much the same since I was doing this same thing with a 1973 Chevy Cheyenne Super one ton. (That was a good rig, wish I had never sold it.)
First off, I have a well maintained 1999 SE with a manual transmission. It was bone stock when I got it. Less than 80,000 miles. I keep it tuned and repaired. Tuned and repaired is important.
I added front and rear tow hooks. Stock Jeeps don't come with appropriate attachment points for recovery gear. You need to be able to pull from the front and the back.
I put a good set of all terrain tires in the stock size on it. Street or Mud and Snow tires won't cut it. Note that mud and snow is not the same as Mud tires.
I have a basic set of mechanics tools and supplies in a surplus canvas mechanics bag.
A five gallon bucket contains a tree strap, a tow strap, 25' of 3/8" binder chain with chain hooks on both ends. Several shackles in appropriate sizes, a lift-mate attachment for the farm jack, two shorter pieces of chain set up for converting the farm jack to a winch and a farm jack base plate.
I throw a good d-handle shovel, an axe and occasionally a machete behind the front seats.
2 1/2 gallon water jug.
First aid kit.
Farm Jack, maasdam jack-all (this is really controversial and it's a dangerous tool)
A day pack with enough basics to keep me going comfortably for 48 - 72 hours.
A multi tool in the glove box. (Best invention EVER!)
Detailed map book, compass and good GPS. (I've had my GPS hack a hairball on numerous occasions for one reason or another. USE A PAPER MAP!)
Coat, down vest, extra set of socks and wear good boots. At some point you are going to have to do a bit of hiking.
Good flashlight, or two.
Make sure your spare is in good condition and at least is the same size as your road tires.
I carry a firearm. That is entirely up to you though. We have predators, both two legged and four legged. It's a low probability that you would ever have a problem, but if you do, it's a serious one. There is essentially no Law Enforcement out there. Period.
Fire extinguisher.
Tire patch kit.
Good, small 12 volt air pump.
Oh, a roll of TP in a plastic bag. (this is getting to be kind of an inside joke, but it is important.)
I hope this long winded post helps you a little. Adjust according to your local conditions and venture forth! You are going to have more fun and adventure than most anything else will provide.