First things first: I am not a big proponent of spending a lot of time and energy filling out job applications online.
That being said, this article about 7 Top Websites For Nonprofit Jobs can be very resourceful. The article outlines different sites that cover a variety of services, from posting job openings to assisting in nonprofit management placement.
I would discourage anyone from relying on these kinds of sites to GET the job, however. Where I find these sites to be most resourceful in in helping you identify the kinds of possible careers that are out there you can target and pursue. If you know you want to get into the nonprofit world, these sites are a great way to brainstorm the possibilities.
But if you come across a job you want, I recommend doing all you can through Linkedin contacts or other networking methods to find out more information about the position and how you might get your foot in the door. Simply applying through an online application is still one of least likely ways to land your dream job.