With the driver, most golfers play the ball too far forward and stand too far away from it. This might feel powerful, but it sets some bad things in motion. The forward ball position shifts the shoulders open to the target, which leads to an out-to-in swing and usually a slice. Standing too far from the ball pulls the upper body downward, leading to a compensating stand-up move through impact, another common cause of the slice.
Here's how to make sure your ball position is correct. Tee it up in line with the logo on your shirt, or just inside your left heel. (For shorter clubs, the ball should stay in line with the logo, but the stance should be narrower, making the ball more centered relative to the body.) As for distance from the ball, the butt of the grip at address should be about six inches from your body. Check this by setting up and then taking your right hand off the grip, moving it about a foot to your right. You shouldn't feel like you have to reach to put it back on the club.
Playing the ball in the correct place takes no athletic ability, it's just remembering to monitor it. Get it right, and your driving will improve immediately.
It's true that a fast takeaway can ruin a swing, but I see more golfers who start too slowly and then kick it into another gear halfway back. That throws the swing out of sync worse than the fast start. Check out the great players: From fast-tempo swingers like Nick Price to slow-tempo guys like Ernie Els, they start at a pace that matches their swing. Smooth is good if that fits your overall rhythm, but never start slow.