You have to know which years and certain parts to avoid. Jeep makes a great product, but they definitely had their bad years during Daimler ownership and transitioning out of that era to now. The JK is the best Jeep yet, but there are a few years with quirks, I will list them below:
--Early JKs had major issues with oil consumption due to rings and connecting rods being installed wrong, 2007 and 2008 models were worst affected, with some early 09s being hit as well, all these engines have since been replaced or died by now, and all 3.8s use a little oil due to the PCV setup, but this normal usage is nothing alarming.
--2007-2011 JKs have one MAJOR flaw and that is the oil cooling on the 42RLE automatics! READ THIS PARAGRAPH IF NOTHING ELSE!!!! The factory oil cooler for this 4spd unit is NOT adequate for offroad driving and has been the cause of many documented cases of fires. What ends up happening is the 42RLE transmission will overheat easily, particularly when driving in sand, and once it hits a critical temp, the oil will literally boil up and out of the dipstick and spill onto the hot exhaust manifold and start a fire. What needs to be done to fix this is to install an aftermarket external oil cooler and flush the transmission fluid with fresh oil. Every time it overheats the oil loses its ability to cool down the transmission and function properly, and increases the risk of overheating and thus increases the fire risk, and its very easy to overheat the 42RLE as it is, much less with compromised oil. This issue is even more prevelant because of the fuel mileage friendly gear ratios used in the Sports.
When Jeep introduced the new 3.6L engine and new W5A580 5spd auto in 2012, they also included a large external oil cooler for the W5A580 transmission, so this problem is fixed on 2012+ automatics, and the manuals never had this issue, and since they don't use ATF (the manuals), never were in danger of this problem.
--If running tires 35" or larger, take particular care of the front axle housing, it tends to bend at the knuckles if the tires take a big hit, and there have been some cases of the front axle tube breaking in half on the passenger side in between the upper and lower control arm mounts. This is fixed by getting axle tube reinforcement plates you can weld on by numerous aftermarket outlets. Some Jeeps have suffered broken Ujoints from losing their bearing caps; For some reason the JK shafts don't like their C-clips. Jeeps driven properly don't usually suffer this issue, but take a big enough hit on the front end with 35s and up, and you might find yourself with one of these issues.
--All JKs suffer from a very weak transfer case shifter linkage design. The linkage itself holds up fine, but the plastic bushings which also double as retainer snaps on both ends of the linkage will break and fall out regularly. There are many ways to fix this as well as aftermarket linkage kits available (advanced adapters has a kit, but pricey $$$). I fixed mine using a cut down plastic OEM bushing (getting rid of the end that 'snaps' on the bushing so it only has one function now instead of 2) and following that on with a washer and cotter pin, hasn't slipped off since and cost $0.15.
--2012 JKs suffered an issue with their cylinder heads involving bad valve guides I believe it was, which was recalled and dealt with, but if you ever hear of this issue, that's what it was regarding.
--2007-2011 JKs had a particularly vulnerable air intake which sucks in water very easily if you drive at any kind of speed through water. Take extra care, in water crossings, not to splash too much into the engine bay, as the hood practically channels water to the air intake. A snorkel obviously remedies this issue. 2012 and up JKs have a redesigned air intake which introduced a splash guard over the opening to redirect water away from the intake.
--2007-2011 JKs have completely unprotected Evaporation canisters underneath that can be torn off by a well placed rock, while not a too common occurance, skid plates for this are cheap enough and it avoids a headache on a longer trip. 2012+ JKs have a factory skid plate for this now.
--2007-2009 JKs seemed to have suffered a high number of quality issues regarding their manual transmissions, mostly relating to popping out of gear and clutch problems. There was a TSB issued for incorrectly manufactured synchro rings on some NSG370 units causing the largest issue and some simply had stiff shifter boots that pushed the stick back. The clutch problems primarily surrounded the throw out bearings, which tend to be noisy. Mine is on my 2011, but it still works fine at nearly 50k miles, some had noise so bad on their earlier JKs, it sounded like imminent failure. The rate of TOB issues has gone down drastically the last several years.
--2007-2009 JKs had a small batch of bad TIPM modules that would go bad causing the "posessed JK" issues where the body related functions would go haywire, including random horn honks, lights flashing and wipers going randomly and all at once if the module completely died, looking like herbie crapped himself.
--ALL JKs, suffer from loose door latches. After some mileage, you'll begin to notice the doors rattle on the latches. Easily fixed by wrapping electrical tape around the latches on all doors (including tailgate) where the latch grabs and you'll have quiet doors hence forth.
--ALL JKs, have crappy a dome light that rattles easily with bass even on the base stereo headunit. I found taking out the dome light and running electrical tape around the soundbar housing where it sits fixed the rattling
-- ALL JKs have THE WRONG SIZED BOLTS used in the suspension components! Can you believe that? Primarily the trac bar and control arms have smaller sized bolts than the actual holes allow for, which was a huge source of the death wobble issues JKs faced. Jeep's answer was to recall all JKs and double the torque on the bolts instead of simply replacing them. Not only that, but the bolts are FULLY THREADED and not shouldered, so WHEN they do come loose, they wallow out the holes making even the right sized bolts useless to fixing the death wobble. Its advised to simply replace all the bolts with the right sized ones ASAP to prevent any damage to the mounts and you can keep that evil death wobble monster at bay. Kits are available or you can source the right sizes yourself from a local hardware store (use grade 8 ONLY! and American made steel!)
--2007-2008 JKs had issue with spitting fuel back out of the filler due to ethanol in the fuel damaging some of the valve components in the tank, this became a TSB and Jeep did replace some tanks with an updated unit that fixed this issue, but since it was not a recall, not ALL 07-08 JKs have had this fix; if yours does this, this is why.
-- ALL JKS -The wiper motors are a bit exposed to the elements in the cowl panel, and some have succumbed to corrosion already, while its not an immediate problem, I imagine most JKs will start suffering wiper motor failures around the 10 year mark as rain water constantly drips on it, unless Jeep has since redesigned it, but this I am unsure of.
-- ALL JKs -The electric motors for the radiator fans are NOT weather sealed! If you do a lot of water and mud, they will fail. Its best to replace it with a fan designed with a sealed motor.
-- ALL JKs - The tierod ends and balljoints are made a lot more cheaply than they used to be. People who run 35"+ tires or offroad hard, have experienced some TRE and balljoint failures. There are PLENTY of aftermarket solutions for this, so its a recommended mod if you plan to take your JK out into the Sahara or equally remote terrain.
-- ALL JKs - it seems to be entirely random which units suffer this issue, but some will have problems with their tops (hard and soft) leaking water when it rains. Mine leaks off and on depending on how I put my top back on last I had it down/off.
Other then that, JKs are solid lol. Granted, do realize this list is a collected knowledge base of recorded issues, but no JK has suffered ALL of them, and most are isolated to earlier years of the JK when Chrysler was owned by Daimler and going through bankruptcy. Despite what most want to believe, Fiat's ownership and constant willingness to give Chrysler all the cash it needs to make better products now-a-days has lead to an increase in quality control with all their products and the JK. Major issues have disappeared and some smaller still remain, but you can thank Daimler for that.
I have a 2011 6spd sport 2dr with almost 50k miles that I love dearly and have had no issues at all, I'm running a 2" lift and 33" KM2 MTs and have been all across the US (moab 4 times) with no failures of any sort. So yes, I do trust my Jeep and see no reason to drop that trust any time soon.