Very few machanical problems.
Replaced valve cover gasket.
Routine maintenance items (plugs, wires, brakes)
Steering wheel wore through after 280,000 miles.
Although it is now beyond its prime, this car seems to be invincible. I bought it from my employer (it was my company car) and it had been seriously neglected. The oil hadn't even been changed in 40000 miles!
Once I got the car, I merely changed the oil and flushed the fluids and put it back on the road.
It has started leaking and burning a little oil, but what would you expect out of a car with this many miles.
This car has continued to run for me with a minimum of expense. In the past eight months (52000 miles) I have spent around $400 on the car. This includes oil, transmission service, tires, brakes, and misc. service parts. Not bad.
I would have to say that you are one lucky dog. My 1997 is nothing but trouble, and everything goes wrong. The speedometor doesn't work, the odometer is broken, it rattles going over 40, wheels shake, trunk leaks, battery dies...don't get me started. Everyone I know with a neon has regretted it. I say you are lucky, but beware... the day will come when it will not start.
I'm glad to see I'm not the only one with a neon that simply will not die. My 1997 Neon has a mere 447000Km (203000miles) and simply refuses to die. Tune-ups and oil changes is all she requires to live on. Blew head gasket once however not replacing your PCV valve after 150000 some miles will do that do a car that often sees the redline.
Best of luck with your neon!