I bought a 2004 Dodge Neon SXT in March of 2011 while I was living down in Georgia, and the car had a little over 90,000 miles on it. The gas mileage was great, as it averaged about 28 miles per gallon on the city and about 35 miles on the highway. It served its purpose, as it was not only a commuter car, but I drove it 2000 miles back to Montana comfortably, with no problems. The car never burned oil. My underlying problems, however, was that I had to replace the motor mounts, and the check oil light came on soon after I bought the car. I also had to change the alignment twice. This is all before 100,000 miles. The suspension wasn't great, as it felt it was metal on metal at times.
Gas mileage and handling are about it. It's a great first car for somebody; however, it's a vehicle you shouldn't consider owning through the long term, unless you enjoy working on cars.
I really don't think the Dart, which is the Neon's predecessor, is a big improvement. Dodge cars aren't built with the quality of Chrysler or Jeep vehicles. Anyway, I am glad I sold this Neon before more problems started to occur. I spent half of the cost in maintenance, such as batteries, tires, motor mounts, oil changes, transmission flushes, alignments, all in the first and only year I owned the vehicle.