Most FLOSS projects probably could benefit from the structure and services that a NPO could provide. However, whether or not you need to start your own NPO to gain these services is a different question. We'll try to address both issues in this document.
Some of these are valid reasons for needing non-profit status, but that doesn't necessarily mean you have to start your own. In fact, you may find you are much better off working with an established NPO that can lend you expertise in many of these areas. By housing many projects within a single corporate entity, there's less burden on any one project of maintaining the corporate infrastructure and understanding changing legal nuances.
There are many organizations which exist purely to accept FLOSS project as members or other types of affiliates so that your FLOSS project can get the benefits of having a NPO without creating your own NPO. These organizations are sometimes called "umbrella organizations". Another common name is "fiscal sponsor", although this can be confusing because such an organization neither gives you money nor necessarily even helps you raise money.
Software Freedom Conservancy (Conservancy) is an organization that exists primarily to be the umbrella organization for its member projects. As such, it is effectively the composition of its of member projects. When a member project joins the Conservancy, it becomes part of the Conservancy. (Although it's not a perfect analogy, the relationship between the project and the Conservancy is roughly similar to a division of a company.)
Conservancy's management oversees, monitors and handles all payments, invoicing, and collects all donations that are made to the project. However, all actions that the Conservancy takes on behalf of the project are recommended and/or approved by the project's leadership.
The FLOSS project maintains all control to make all technical decisions.
SPI is a non-profit which was founded to help organizations develop and distribute open hardware.
If you still feel that you need your own non-profit, there are many things to bear in mind. For an overview of many of these topics, see the excellent
primer published by the Software Freedom Law Center.
In the US, there are two IRS classifications which non-profit organizations in the free software space have registered under. Most common is the 501(c)3, but also there's the 501(c)6. Stormy Peters wrote a short article on the differences between the two.
Philosophically, a 501(c)3 is set up for the benefit of the public, whereas a 501(c)6 is set up for the benefit of its members. Therefore, in the (c)6 case, your governance structure and who becomes a member is correspondingly more important.