Fuel Pump - This is mainly my fault, I always used to run the tank almost dry every time. Don't do this, the fuel pump is INSIDE the gas tank, an the gas acts as the cooler for the fuel pump.
Rear Main Seal - This started leaking at around 100,000 miles.. It's a $12.00 part, but it'll take me a few hours to drop the transmission and replace it. I lose about 1-2 quarts of oil every 1500-2000 miles. It's gotten progressively worse.
This car has been very good to me. Last year I took a 2000+ mile roadtrip, taking me through the Mojave Desert with temperatures exceeding 110F degrees. This car handled it with no problems at all.
I see a lot of bad reviews of this car, but I LOVE my car and will keep it until it dies. I know dozens of Neon owners (I'm a member of the Neon Enthusiasts Club). There are thousands of happy Neon owners all over the world.
I owned a 1998 Neon until January 8th 2004. My Neon was well cared for and except for regular maintenance, I had no expense using this car. My sole complain comes from a place which we hope will never occur to us. I was, unfortunately, involved in a collision with my Neon. I hit another vehicle with my front right side, going at about 40 mph and on impact the car went up in flames. Luckily for me There was an experienced paramedic driving behind me and he stopped and pulled me out just before the car was engulfed in flames.