A lot has already been touched on, and you have some great answers.
When I went to 37s (Heavy Toyo 37x13.5) the first thing that went south were the rear flanges, then ball joints, then unit bearings, then the steering (TR & DL). I had added the Artec truss kit which comes with beefed up skids for the control arms, etc. That Jeep always had something wearing out or breaking. It was frustrating.
The lessons I learned from that Jeep was to bite the bullet and make upgrades up front. So the next Jeep we installed a aftermarket axles D60/D44, big brakes, steering, etc all up front. It's been great for 70,000 miles with no issues other than a leaky rear seal. Running a 37x12.5 lighter Cooper
Hindsight, I would have done full float axles and all the fixins up front. I prefer to be overbuilt from the viewpoint of durability (more than capability) which is pretty much what coilrod said in post #7
So back to Jeep #1 above, it's currently pulled apart getting full 1 tons, steering, brakes, etc. It was a long, winding road for me and I prefer to learn my lessons the hard way. In the end I spent WAY more money on that Jeep adding things onesy, twosy, and also had a lot more downtime.
I second this advice. It is a lot of money to do 37s right/dependably on stock configured axles. But it is far from optimal and actually has many shortcomings. I wish I had gone with better and wider axles from the beginning. I would have spent a lot less money even if I had gone with crate axles but I was headstrong. Now that I'm on 37s on standard width axles I see a lot of the shortcomings. I'm kind of stuck going down the path I'm on but it was easier (although not smarter) to spend more money over time for a compromised setup with 37s.
I kind of wish I had stayed with 35s and totally maximized everything to take advantage of that size tire. I would have picked aluminum for all my armor and just stayed with mild Dana 44s and spent a lot less money and had a more nimble and fun vehicle.
Another issue with 37s or larger tires is flex/articulation. As the tire size goes up, there is a reduction in up travel unless you start trimming and/or adding high clearance fenders. At 37s with Metalcloak overline fenders I lost 2" of up travel so I lowered my 15" 6pak shocks to regain lost shock travel. Now I have 31" of shock extension when compared to stock mounting location. This added droop to retain good articulation has caused; front driveshaft and exhaust clearance issues, rear driveshaft operating angle issues, unseated coil springs, driveshaft and gas tank clearance issues, wiring and cable and hose issues, reduced backspacing for tire clearance, accelerated bushing wear due to increased angles.
I do enjoy my 37s but there is a lot more maintenance and I regularly damage something because I am trying a lot harder trails to feel challenged. I'm at 2.75" backspacing to get the clearance I need. My gas mileage has tanked and I average 13.2mpg over the last 3 years. If I won the lottery I would still stay in this tire size range (38s sitting in storage) but would buy 70" wide Hi-pinion Dana 60s front and rear in 8x6.5" bolt pattern and go back to 4.75" backspacing.
Here is a list of parts during my path to 37s: (does not include lift parts)
Terra44R front housing, 5.13s, RCV shafts
Teraflex knuckles, balljoints (2 sets), 2 sets of hub bearings (I've been lucky), high steering and front big brake kit
Crown larger master cylinder (not J8 complete booster and mc kit)
Synergy sector shaft and TB brace (before hydro assist)
PSC hydraulic assist kit with big bore box (still using Synergy TB brace)
Teraflex 8x6.5" front locking hub kit and Teraflex inner shafts (Not installed yet)
G2 rear axle shafts, 5.13 gears
1310 front and 1350 rear driveshaft (1350 doesn't have enough operating angle for my rear suspension)
Mini rear stretch and new relocated heavy duty brackets
Synergy rear track bar brace
Teraflex rear full float 8 lug kit (not installed yet with larger rotors)
Artec Apex truss (not installed yet)
KMC 8x6.5" beadlocks and 38" Patagonia MTs (not installed yet)
I really do enjoy my Jeep but if I had more self control I would probably be 20k+ richer and I would take pride in doing more with less tire size.