I would and I have signed a non-compete, but I did not want to. It was very unfair to me as I could also be laid off or fired at anytime for any reason. It made it very hard for me to find a new job when they finally let me go.
While I do not like non-compete agreements, I can see myself signing one for practical reasons. If I really wanted a particular job -- say, my dream job -- but I had to sign a non-disclosure or a non-compete agreement to get it, I would sign it. Thank goodness Obama's administration is trying to make these agreements illegal!
It is reasonable that big companies might ask their employees to sign non-disclosure agreements if they move to a rival company but it is not fair to restrict their employment options in the future. Companies 'poaching' employees tend to offer them a better deal than they have at the present. Non-compete agreements remove the responsibility on the company to treat and pay their employees adequately.
This country was founded on freedom. Healthy competition among companies will keep them on their toes. This will benefit the employees since the companies will have to work harder to keep them. If the companies are worried about trade secrets, they can protect themselves by requiring employees to sign non-disclosure agreements.