As with any motor, the answer, in part, is obviously "it depends on how well it was cared for." I have a friend that totaled a 99' Ram 1500, 4X4, 5.9 with 330,000+ miles on it. It smoked a little at start up, but ran very good. I'd speculate that it would have easily gone to 400,000.
EDIT: Look around ebay, craigslist etc at older Dodges. There are countless out there with 250,000 miles on them, still running strong. If the transmission on that '03 hasn't been rebuilt, it's probably due.

Probably same issues as the Chicago area. Rust. I have still, an 03 durango 4x4 that looks and runs great at 175k mi. The eng is a 4.7, but I could take either eng as I can rebuild if needed. The 4x4's usually have the wide wheel opening flares that can hide the wheel opening rust in any of the 4 wheel openings of fenders. If you see rust-paint bubbling creeping out from under those body colored flares, the rust is probably real bad under there. One of the first rust areas is at the front fenders right above the bumper wraparound area. They rott there quick. Only real annoying failure is the flimsy easy break window track cable pivots whatever, that like to break mostly in winter when window is froze. Not sure if the 03 plenum gaskets were better than older either.

Im on my 5th "Square body" Dakota. 1st was a 90 2wd longbed w/a 3.9 then a 94 shortbed reg cab w/a 3.9. then a 93 CC with a 318 that I converted to a stick. I miss that one every day but it was wrecked. Only had 202K on it, had no intention of getting rid of it. I replaced that with a 92 CC w/a 318, still driving the snot out of it, not as good on gas as the stick one was (same gear ratio too) but no worse than the 94 with the 3.9.
A week and a 1/2 ago I found a very clean (especially for IL/NW Ind.) 96 4X4 club cab on CL in Dyer Ind. and brought it home. cab and bed like brand new. doors juuust starting to bubble at very bottom. Only rust hole is bottom of dogleg on pass. fender. I got it cheap because the trans was laying in the bed. Now that trans is apart on the bench. I can rebuild it and replace the converter for less than most junkyard trannys. I plan to keep both the 92 and the 96 til I run them into the ground.
You could not give me a 4.7 or a Quad cab, with its worthlessly short bed.
At nearly 6' tall I could never climb in the bed when I am on a campout and get rained out of the tent, has happened more than once. and then lumberyard runs with a just-over-5' long bed, just do not work.
Another reason to stay with an older truck; I have absolutely no desire for a 4 door truck, but that's all that can be found these days. and you want a stick? FORGET ABOUT THAT!
as a rule, it seems that of the square body ones still on the road (that I see, anyways), they are still in better shape body wise than the next gen 97-04s.