Most college based accelerators don't take equity - MIT's delta , Stanford's Start X and McGill's X1-Accelerator are examples.
In addition there are also several accelerators run by non profits or corporations that don't take equity. Examples include
An undated Startup Freak article lists a number of equity free accelerators all over the world.
New programs come up all the time, including accelerators that are backed by government organizations (including many international options), non profits, for-profit corporations, venture capital firms. We suggest you do a web search on "equity free startup accelerators" to find updated lists of accelerators that may meet your needs.
This article builds on content developed by the Martin Trust Center for MIT Entrepreneurship for MIT's Orbit Knowledgebase and is licensed under CC BY-NC-SA 4.0.