Exhaust manifold cracked around 15,000 miles. It took the dealer two tries to put it on correctly (under warranty).
Faulty fuel gage left me stranded far away from the nearest phone. Wasted a lot more time having it towed and then waiting in lines at the dealer because I couldn't tell that it just needed more gas.
Air conditioner leak in front passenger seat area fixed by me thanks to information found on similar forums. The dealer said they couldn't do anything about it.
Replaced "sealed" hydraulic clutch line system just before the 36,000 mile warranty expired. At first the dealer denied it as a warranty repair because the problem was caused by "too much mud". The repair was finally covered after a long argument about whether or not Jeeps are intended to be taken off-road.
Rear brakes replaced at about 40,000 miles.
Clutch went out at around 45,000 miles.
First and second manual transmission gears broke at around 49,000 miles.
Slave cylinder replaced at around 52,000 miles.
Starter replaced by me at 55,000 miles.
Current problems (at 58,000 miles) include:
Leaking gas tank.
Stalls while driving (seems to be an electrical problem).
Front suspension joint pops off if at the wrong angle.
Four wheel drive makes an awful grating noise when turning the wheel.
And of course, the zippers don't work on the soft top windows, but I've re-sewn a new zipper on one side so far.
My previous vehicle was an old Jeep CJ -7 so I've got no problem with the noise, bumpy ride, or lack of any other car-like comforts. Those help make a Jeep a Jeep.
And, when it runs, it's the perfect vehicle to me. It's quick, great fun with the top down, and can four-wheel with the best of them.
However, I think they are made up of cheap parts and are put together poorly. I don't feel comfortable taking it off-road or even on long highway trips anymore because of what might break next. That said, I was happy when my warranty expired so I didn't have to mess with the dealer anymore and was free to upgrade it with better parts.
If you are thinking of buying one, they are a lot of fun. I haven't been able to get rid of mine yet. Just be prepared to either spend a lot of time fixing things yourself or at the mechanic's shop. Also, the 6-cylinder is worth every penny more than the underpowered 4-cylinder.