Egg-fried rice is a brilliantly simple accompaniment to all kinds of Chinese dishes. The secret of all good home-cooked Chinese food is a well-seasoned, extremely hot wok. The rice won't stick at all if you get this right. You'll know you've got it hot enough because all the hairs on your hands will be incinerated.
Woks are a very personal thing. Personally I hate non-stick ones, as bits of non-stick coating falling off and contaminating my food tend to ruin the eating experience. The only alternative I've found to a good traditional steel wok, expertly seasoned, is an anodised aluminium one.
It also helps if your rice is very dry and chilled. Rice shouldn't be left at room temperature for any length of time anyway, or it's possible it'll kill you, so try to rapidly chill it after boiling. This results in firmer grains which fry beautifully in your perfect wok.