STEALING IS WRONG.
Newspaper vending machines are painfully easy to rip off. I believe that this is due to the fact that it is simply not cost-effective to invest in new security measures for a box that has maybe 50 cents worth of paper in it. Please note that it is even less cost effective to go to jail for stealing a newspaper.
There is more than one way to skin a cat, and there are several ways you could go about getting a newspaper out of a vending machine.
The idea that occurs first to most people is to simply pay for one paper, then take more than one. The problem with this, though, is that you still have to pay for one, and there's not a lot of use for multiple copies of the same newspaper. If you sell one, you can recoup your initial investment, but is it really worth all the trouble?
If salesmanship is not your forté, perhaps brute force is. A hammer and a pointy thing will make short (if violent) work of the plexiglas window on the front of the machine. Either that or you could apply a hacksaw to the latch. This method is even more trouble than the previous one, and it does not come recommended.
Let's suppose you don't have any money, and you left your toolbox at home, but you really want that paper. There's still hope for you. Press the coin return button on the machine. While holding this button, yank the handle firmly. The door should open. Now, don't touch any of the papers inside, and close the door. Gain satisfaction from the knowledge that you've rooted this box.