Ah ha - I found the invite in my inbox. So perhaps if you have been invited, make sure you are logged into Gmail and go to the Google+ page and see if it'll let you in, it might just be the shove the system needs to open its doors.
FYI-- If you've gotten a "backdoor" circle invite from someone, and you couldn't join with it previously, they've currently got the process throttled back open in some instances. If you've got said email w/the conversation link in it still, you might want to give it a try again if you couldn't get in initially.
I just sent invites to more people on this thread who asked. Also, I did it by adding them to my "invites" circle and when I added them all a little button showed up that said "Send these people invites?". I clicked it and it responded with "invites sent". So they may have opened it up again for a bit.
**UPDATE** Anyone with an account can invite people now (as of 9pm PST). Go to your "home" page on G+ and there should be a button on the lower right of the screen to invite people.
I'll also come begging here for an invite: williamalex(dot)cunningham@gmail(dot)com.
In return for an invite, if you have a picture up here somewhere I'll draw a sketch of you being awesome somewhere like in space or dinosaur times, and put it up on the Draw Each Other thread for all to envy you.
If you do not have a picture and are afraid of your image ghoulishly frozen in pixels and hung in metaphorical suspension in digital non-space to be leered at by souless avatars, then I'll just be your google+ friend, I guess.
Well shit, that didn't last long. The invite button has disappeared.
@oddbill I'll send you one as soon as it opens up again. I'll also try the backdoor approach so even if you don't receive an email in the next little bit it may not hurt to try logging into the site anyway.
Whoever wants to add me on there, my email address is joshua.catlett at gmail. I'm working a lot of hours right now, so I probably won't use it too much for the next couple of weeks, but I really like the interface and most of the rules behind the system. I'll probably start posting like I do on Twitter once my work hours go down.
@everyone requesting invites - I work odd hours so will continue to send out the backdoor "invites" once or twice a day until actual invites are reopened.
I believe I never mentioned my actual e-mail address before. mike.a.townsend at gmail dot com if anyone ever gets invites again. I can't draw like oddbill, but if it takes bribes, I could make you a character in something. Or if you don't mind waiting a couple of years, I could write you a song. Or just drink to you. Heck, I can definitely promise to do that.
@taphead - I've already seen something regarding x-posting capability into FB. Given Google's nature, I'd lay odds that they will eventually allow at least indirect implementation (if not directly implement it themselves) for that sort of active flow through between the various mediums.