There are few ways to earn bit coin without investment. They are
1. Doing an online freelancing job like website designing or logo designing and request to pay in bit coin. One such website where you get a freelancing job is
www.xbtfreelancer.com

2. Sign Up Bonus for Alt Coins, Air Drops and Bounties - Check out the Services Place in the Forum
https://bitcointalk.org/index.php?board=52.0

3. Faucets - Most Time consuming with least reward. Not Recommended.