Neon tetras must be one of the most popular fish after goldfish due to their availiability in fish shops. Neo tetras have a brilliant flouro colour stripe on their body when they are healthy and happy. When the become pale, it means something is wrong (usually the water).
Neon tetras are best kept in a big group for best effect.
One thing to note is there is a 'neon tetra disease' which is said to be incurable. If you have neon tetras die one by one day after day for apparently no reason (and you are sure it is not water quality), neon tetra disease is a possibility. In such cases, quickly discard dead fish before the healthy ones can eat them. Also, remove all neons that look like they are sick (inactive, not schooling with the rest etc) into a separate hospital tank.
There is another tetra that looks like neon tetra, it is called Cardinal Tetra. Their blue/green flouro stripe does not curve or taper off to the tail like the neon's, but instead theirs is straight and horizontal and extend all the way to the tail. Their red is also full lengthwise and does not start from halfway like neons.
Note: Cardinal tetras do not contract 'neon tetra disease' and there is no cardinal equivalent of the disease.