I have owned a neon for the last 2 1/2 years, still have it (for sale) with 120k miles on the clock and still going strong. I love mopar cars, and that is as unbiased of an opinion as you'll get. My family hates dodge, I gave one a try and loved it. As always, a lot depends on whether the car was taken care of or not. All brands make lemons, and all vehicles will break down if neglected. With Chrysler products I have found quality where it counts (no electrical problems, good engine, decent tranny if you don't abuse it, etc...) but expect to find corners cut in non essential areas (cheap interiors, dash rattles, wind noise, minimal sound insulation compared to other vehicles in class, etc...). My neon did not have an easy life (frequently saw 7000+rpm, power shifts, and a few 5000rpm launches) yet held up well. Only item that needed replacing other than normal maintenance issues was the EGR solenoid, which got blocked off a year later. With the 2.0L engines in the neons, the only things to watch for are headgasket failure, and if the timing belt breaks you will bend valves (interference engine). Headgaskets were faulty from the factory, check between cylinders 1 and 2 on the front side of the engine between the head and block for a metal tab, this signifies the MLS headgasket which is a quality unit. If the car is a '98 or newer, or has over 100k miles it is likely to have the MLS headgaket. The 2.4L DOHC is also a non-interference engine I believe (but don't quote me on that) and uses the same head as the 2.0L DOHC, same bore, but a longer stroke and 1" taller deck height. In my opinion, the 2.4L is a very good engine. Smooth, torquey, and reliable (and you can also make them put out 200+ hp fairly easily). If the car appears to be in good condition, looks like it was well maintained and is at a reasonable price, I would not hesitate to buy it. If you have a way of checking the VIN that might be a good idea... I've found US made Chryslers to be of better quality than the Mexican made ones. Also, you can check the computer for stored codes by flipping the key on-off-on-off-on within 5 seconds (on position only, do not start). If the vehicle has a digital odometer/tripometer the codes will be displayed there. Otherwise the check engine/service engine soon light will flash out a series of two digit codes, with a short pause between digits and a longer pause between codes. Take care of it and it should take care of you.
I apologize if my post was too lengthy.