I purchased my Neon on April of 2000 and I've put 35K miles in it. So far I've not had any problem. The car handles beautifully on the road. It's extremely stable on the corners and it has plenty of grip. The Neon is pretty powerful for it's size (5 speed manual) and shifting is pretty smooth. Breaking is also excellent. I've been involved in an accident a year ago and the car handled it without a problem.
I'm very happy with it. Simply a great car.
It's hard to find many cars around that handle as good as Neon.