I'd have to say I'm the opposite, I am constantly checking to see if mine sticks out more haha. I'm not even sure why but I would love to have a really prominent Adam's apple.
Although if I were to have one I feel like I'd be more conscious of my neck, like getting hit there. (It's happened a few times, once by a baseball) I feel like it would be so much more painful, or even just really uncomfortable for things to brush your neck.