I've had my 03 7.3 for about a year now, it's been my first diesel. I love the thing, tows anything you can throw at it, always starts right up, and has only been in the shop once since i've had it. Has 140k on it now, stock glow plugs, wiring harnesses, relays...not to bad. I had to have the o-rings under the turbo replaced, which are known for leaking.
Like others have said, commonly rust out, mine is no exception. my oil pan was starting to bubble a bit, but sanded it down, primed it and coated it in rust-fix. cab corners and over fenders are going now.
one thing others haven't touched on are the front hub bearings, had to do them on mine, not hard to do just kinda pricey at 300+ per side.
They do well with simple mods too.
I've got:
4 inch turbo back
6637 intake (the best DIY intake lots of write ups)
Hypertech 100hp tune
HPX (high pressure crossover line, makes idle quiter and smoother)