I'm old school.  I prefer to roll dice and discover a character by what the dice tell me.  I much prefer a system like 1E AD&D where you random roll stats and then see what type of character you have qualified to play.  You can't play a Paladin unless your rolls qualify.
Classic Traveller is another game I love, with a character generation system that is both fun and brilliant.  Life doesn't always allow you to make lemonade.  You may have wanted to be a film director, but, instead, life turned you down the road of being a computer technician.  That's how CT character generation works.  And, it generates some extremely interesting characters.
I love rolling dice and listening to them--figuring out what they mean.  I love to figure out "How did this character come to be this way."
To me that's much more rewarding than systems like 3E D&D where a player can play any class of character, right off the bat, as there's no requirements (which is not always true, especially with prestige classes).
There are a significant number of people, though, on the other side of this who argue, "If I want to play a Paladin, then why can't I?  I want to have fun, too!  And, I want to play a Paladin, regardless of what I roll!"
To be fair, I can see that point.
What about you?  Where do you stand on this issue?