I think one of the most important things about a character is that he brings something different to the table. Whether that be personality, background or what's on your stat sheet. I also think that a World of Darkness character should usually have a little mystery behind them. Different venues stress a hidden past more than others, but being at least a little different than what you appear is something that can be a lot of fun.
Lastly, I think having well definied short term and long term goals for your character makes them lots of fun to play. It colors your character's actions, and gives you a lot of stuff to do in downtime and can make you seek out other characters that you would not normally interact with. A character concept is good, but setting goals makes your character truly alive.