How come some cyclists lean forward at a 45 - 60 degree angle and I don't?
To complement Neil Fein's answer, the rider's position is almost entirely controlled (given a particular rider) by the geometry of the bike.

Compare the following bikes. In the first image of a hybrid bike, the saddle is slightly below the handlebars. In the second image depicting a road racing bike, the saddle is well above it, forcing the rider to lean farther over to reach the lower handlebar position. In the third image of a time trial bike, the seat height and handlebar height have remained relatively unchanged, but the seatpost is at a much steeper angle and the intended grip brings the arms much further forward, forcing an even more horizontal position in order to put the hands on the bars.





Now look at the riders in this next series of images to better see the difference.


(source: bicycledutch.wordpress.com)


(source: www.flickr.com)


(source: bikesportmichigan.com)