As long as you do fuel filters religiously and change your oil you "usually" will stay pretty trouble free. Other than that I recommend doing an EGR delete on a 6.0 basically as soon as you can. Once the coolers block up they superheat the coolant and blow head gaskets. They are also prone to IPR valve failures (they regulate the high pressure oil), high pressure oil leaks (o rings, SCT fittings, injector o rings, branch tubes, etc.), and FICM failures (about $700).
My brother bought an 03 that didn't run for $5500 and I put a FICM in it and it fired up and ran. Threw a code for low contribution #7 so we put an injector in #7. Code kept coming back so he got a relative compression test done with the Ford IDS software and came up severely low on compression in #7. Wasn't using coolant but was using oil. He found a 12 valve to replace the engine with and after pulling the head off the 6.0 when we got it out, we found the wrist pin clip had broken and the pin was cutting a groove through the cylinder wall and the rod was also slightly bent.
The 12 valve swap is done now and he loves it. We removed the 5R110 because he was told by a few transmission builders known for ford transmissions that the 5R's don't really like the low end torque a cummins produces. He ended up getting a John Wood? (I think that's his name) 4R100 and converter and a PCS controller. I tuned the PCS and he loves it. The PCS' program can get a little confusing for some but is actually pretty simple if you have a general understanding of what the transmission is doing, or trying to do, and what the sensors should be seeing and when. The tune ability is great and is nice because you can tune it while driving down the road if you want. Or you can datalog and have PCS' techs make changes for you through e mails sending programs back and forth. I wouldn't be scared as long as the body isn't shot. Just always keep a 12 valve hidden away for when the day comes... Lol