I love crafting new characters. I always have since my first roleplaying chats to wrestling with the latest M&M rule-set until it did what I wanted.
I build characters in one of two ways:
Create a concept and then try to stay as true as possible inside the realms of the systems. This usually works better with point-buy classless systems. But if you know the system/setting it can work with anything.
Build a character mechanically and allow the choices to build a story in my mind. I prefer this method when I am unaware of the setting, among other things because it allows me to pour through the flavor text of my option and learn enough to actually build the character AND fit him in the world.
I must admit to a weakness for randomized chargens though. Because it liberates me from choice making and I can delve completely into the art of fleshing the character out.
I love it not only because it saves me from over thinking my choices, but also because it acts as a shield against the efficiency bores that like to comment on my builds. “I didn’t choose to be this gimped, blame the dice.” Now, of course I generally draw the line at a character that is so self-limiting he might as well just roll over and die, but it allows me to experiment with suboptimal (and thus hopefully, interesting) characters that even I would have not thought of before.
Some of my favorite randomized chargens are those of Teenagers From Outer Space, the random monster rules for Monsters and Other Childish Things and Dark Heresy (and the whole 40k series for that matter.)
The result of my latest encounter with randomized chargen is Mir, the Imperial Psyker of Feral origin. I rolled everything except the career path (because I wanted a psyker). He’s going to see play for the first time today, and to get a better idea of how his mind worked I wrote this: Personnel Files. I’m not completely happy with the second part, but I think I definitely have a better feel for the voice of the character.
May you dice land on the table!