The 7.3 is an extremely reliable engine, with a list of true problem so short that I can list all of them right now. It is not unheard of the hear of these things going 400K without a glitch, but when you have a problem, you can bet it is one of the following:
ELECTRONICS
1.) The CPS (Camshaft position sensor) has a reputation for dying quite often, without warning. It leaves the truck totally inoperable. The good thing is that they are super easy to change, so you can carry one in your glovebox and fix it real quick if it goes. See Wiki for more info.
2.) Glow plug relay - This $40 relay tends to not last long under the high amp loads of the glow plugs. Some guys replace one a year. I've never replaced mine, but my truck does smoke on cold mornings, so it probably needs it soon. Best case, it goes out slow, gives you indication it is going out by smoking and hard starting in the morning. Worst case, it goes out fast, and you can't get your truck started one very cold morning.
3.) Fuel heater- Tends to burn out occasionally. MUCH more rare than the other two items, but the result is the same. YOur truck won't run until you fix the problem. THis happens on maybe one out of 50 trucks, and will only happen once in the truck's lifetime if you're the unlucky one.
MECHANICS
1.) The 7.3 IDI engine (more or less the same as the 7.3 PS mechanically) had SERIOUS problems with cavitation. The problem came from miniscule movements in the pressurized water jacket from stresses related to the high compression ratio of the old IDIs. The movements created sudden pressure drops, causing cavitation in the water jacket 1,500 times per minute, which slowly eroded the cylinder walls until you had holes in your cylinders, and a wrecked engine. This is almost UNHEARD of on the 7.3 PS, and is totally avoidable by simply adding a nitrile additive to your antifreeze at regular intervals. Just for your info, many, many diesel engines, from all manufacturers, have the same problem.
2.) Rods - The stock rods on a 2001 and newer truck will "only" hold about 375 to 400 horsepower before they go. Not a big deal if you are not planning on rodding your truck, but if you are, either plan on replacing rods, or get a 2000 or older
3.) Auto tranny - Like every single diesel truck ever released up until recently, the auto tranny was insuffcient at best behind the high torque of the 7.3. Upgrades are almost necessary, if not highly recommended.
4.) Water pump - they go out a lot. Casting sand from the factory comes loose in the water jacket occasionally, and eats up the bearings. Coolant filters solve this problem. Easier than heck to change out, not really a big deal
THE REST
Best darn truck I've ever owned. Period. Hands down, no questions asked.