What makes a complete character?

As I kick around more Roguish RPG design elements, the notion of what makes a complete character comes up in my mind often.  Stats are a core component, but how many are enough and what role (or roll?) should they play?  Races?  Classes? How many and which?  Background? skills? Special abilities? Region of birth? Height? weight? Eye and hair color? Equipment lists on a page or pages and pages of potential items?

There is so much potential, but how much is too much or simply not enough?  It varies by player and referee, but I fall into the less is more crowd.  Kind of a streamlined GURPS approach of 4 core stats, but combined with the simplicity of a class system. Is there a character generation system or a combination of them, that you feel is the "best"? Please let me know what you do, what you use, and why you like it.