X.Org is not a single thing. One the one hand, X.Org is a collection of projects that provide a window system stack, most notably the X server, its drivers and Xlib. Some other tools are part of the X.Org software set (see the X11R7.7 katamari release). Additionally, there are projects that are more or less associated with X.Org but aren't necessarily X.Org (depends on who you ask, and it doesn't really matter anyway for this post). These projects include Mesa and Wayland. Let's call this the "Software".
On the other hand, X.Org is the X.Org Foundation, a non-profit corporation to help advance X.Org and related projects. Let's call this the "Foundation". Disclaimer upfront: I'm the current Secretary for the X.Org Foundation.
The Software and the Foundation are not the same thing, but they do share the name. The Foundation has zero technical influence over the development of the Software, it cannot direct roadmaps, it cannot decide on releases, it can't decide on technical features. The Foundation does have money it can provide to developers of the Software though. This is done indirectly, e.g. through financing developer conferences (XDC) and providing travel sponsorship for attendees. The Foundation backs the Endless Vacation of Code (think Google Summer of Code without specific start dates).
Generally, what happens with the Foundation doesn't really matter to the Software and that is by design. If the Foundation goes away, the worst thing that would happen to the Software is that funding for conferences would have to come from elsewhere. Think of the Foundation as being the rich auntie for the developers. You can ask her for money to travel, but she doesn't participate in day-to-day development work.
Recently, you may have read that the Foundation lost 501(c)(3) status (temporarily anyway). For the non-US readers, 501(c)(3) is US legalese for a non-profit organisation which allows for some donations to be tax-deductible. The loss of the 501(c)(3) status caused the usual internet outrage and insults towards the Foundation and the Software, so let's look at that in a bit more detail.
The X.Org Foundation structureThere is a link between the members of the Foundation and the Software: to become a member, you have to "i) be actively involved in the activities relating to the technologies of X.Org, as set forth in the Membership Agreement". So as long as you're hacking on X or you're otherwise affiliated, you can join and membership is free.
The day-to-day work of the Foundation are largely handled by the Board of Directors, 8 elected members in two-year terms, 4 of which are up for election every year. One treasurer, one secretary, pretty much standard stuff. The board has regular meetings, but if they get your blood pressure up you really need to see a doctor.
Gaining, losing and re-gaining 501(c)(3) statusThe reason we even have that status is historical. Back a few years ago the old X Consortium got regular chunks money from large corporations (Sun, HP, to name a few). After the change to X.Org, setting that up for tax-deductible donations seemed like a good idea. Fast-forward a bit and with the help of the great people at the SFLC X.Org got 501(c)(3) status in 2012 (retroactively applied to 2009).
Something else happened while fast-forwarding: we never actually solicited or took any donations. The financial crisis had hit, so there wasn't that much money around and anyway we had enough money to run conferences for years to come. The closest thing to a donation we got was to allow interested parties to host beer bashes at our conferences.
So since 2005, we've been slow-burning through money and at the current rate we still have enough money for a couple of years of conferences and travel sponsorship. 501(c)(3) limits the ways how to spend the money (see Wikipedia), so we pretty much only spend it on conferences and travel.
So the summary: the Foundation is a 501(c)(3) that doesn't collect donations. But if we did, they'd be tax-deductible. As long as you're in the US, that is. Non-US people pretty much have nothing to gain either way since we're not registered in any other country and 501(c)(3) doesn't apply to other (any?) countries. (Correct me if I'm wrong. Also: don't listen to me for tax advice)
A couple of months ago 2013 we lost 501(c)(3) status. The reason we lost it: we didn't file the required tax forms. As said above, no donations means no income, so we never actually owed any taxes and we hadn't filed tax forms for years before we go the 501(c)(3) status. So the IRS removing our status was a bit of a surprise. I should also note that the Foundation is one step removed from from the IRS communication: the IRS contacts the SFLC who then contacts us.
Anyway, once again the great people at the SFLC helped us and we got the 501(c)(3) re-instated. So we're back to normal, not collecting tax-deductible donations. With the additional benefit of having learned to double-check tax forms from now on.
SummaryWe had 501(c)(3) status but didn't collect donations. Then we lost it, and got it back, all the time not actually collecting donations. There was no money owed to the IRS. No doubt: It's embarrassing, it shouldn't have happened. But in reality it had zero effect.
So pack up the pitchforks, but keep them well oiled, I'm sure there's a reason to get them out soon again.
Final note: you may have heard that the Foundation is planning to join SPI. This is correct but still ongoing and I'll talk about that when it's actually done.