ORIGINAL: Rick James
Your bow arm should be in the position that creates the least amount of tension in that bow arm. Typically this is done in a straight position, however don't confuse the term straight with "locked" or hyperextended. Every persons body type is different though, so this may vary from person to person.
I personally shoot with a straight bow arm, with the inside of my elbow at a 45 degree angle to the ground, and my front bow arm shoulder low and bottomed out. This is where I develop the least amount of tension in my shot, and where I am most consistent.
Exactly
This post from Greg/MO says it well.
As far as the straight arm... I think the best I ever heard it put was by Michael Braden when he talked about having a bent arm and leaning against a fence post or door jamb. See how long you can hold the weight of your body up like that; then, straighten your arm out to a relaxed state just like it were hanging naturally at your side and see how well you can support your body weight. There's no comparison.