The genre is very old, and has a lot of recognizable games. The most distinctive traits are characters growing in power (by gaining levels and experience points) and some sort of customization (not always appearance, but also skills, equipment, items, etc.). In them, player controls a character (or a group of them) and go on doing quests. Anyway, this sort of games is called Role-Playing Games (or RPGs, in short). I've meant to answer this post for a long time, but I never could get to sit down and do it.
