Invisible Pink Unicorn
The first mentions of the IPU appeared on the alt.atheism discussion group, indeed, "believers" state that the IPU was "revealed" to us on alt.atheism, though there are reports of oral transmission of her stories before her revelation on the internet.
The idea of the IPU was fleshed out by a group of college students between '94 and '95 at the ISCA Telnet-based BBS. A manifesto was created that related the main doctrines, beliefs, and mythology of the IPU. This manifesto was the source of what soon became the most famous quote regarding the Invisible Pink Unicorn:
"Invisible Pink Unicorns are beings of great spiritual power. We know this because they are capable of being invisible and pink at the same time. Like all religions, the Faith of the Invisible Pink Unicorns is based upon both logic and faith. We have faith that they are pink; we logically know that they are invisible because we can't see them."
- — Steve Eley
It's common for "believers" in the IPU to state that, since She's invisible, no one can prove She doesn't exist. This parallels similar statements about the gods of other religions. Thus, this serves as an illustration of the absurdity of using lack of proof as proof of existance. Under this logic the IPU is just as credible as any god.
The fact that the IPU is invisible and pink is a known contradiction, but this too is simply an illustration of the absurdity of the Christian god's characteristics, e.g. being all-knowing, all-powerful, and all-loving yet somehow failing to destroy evil, see Problem of evil.
Another part of the satire is the fact that "followers" hold inconsistent ideas about the IPU's qualities. For example, some believe that she is completely invisible and some believe she is visible to those who have faith in her existence. However, some agreements have been made about her characteristics, for example that she likes raisin bread (symbolizing the expanding universe), that she prefers ham and pineapple pizza (though some vegetarians disagree saying that, since she's vegetarian she wouldn't eat ham, but mushrooms instead). When someone points out this dispute ("If even her followers can't agree on what she's like...") the usual response something like "Well, at least everyone agrees that she likes pineapple!" This parallels the similar Christian response of "Well, at least all Christians agree on the basics" when someone points out the inconsistent beliefs among different Christian sects. Another agreement among IPU believers is the idea that she hates pepperoni. Yet another agreement is the idea that the IPU "raptures" socks which accounts for their strange tendancy to disappear. Thus, when a sock is "raptured" from one's wash it is taken as a sign of favour from the IPU. Some see it as a disfavour, however, depending on who is asked and the type of sock that was raptured.
The IPU religion has a "devil" figure as well in the form of the Purple Oyster. Also known as the "Purple Oyster of Doom" or the "PO(oD)" it's said to have originally been in the service of the IPU but was cast out of her pastures for trying to convince believers that the IPU likes pepperoni and mushroom pizza the best.
In the manifesto, IPUs were said to punish nonbelievers by poking them with their horns. The pain from being poked was typically blamed on mosquitoes which, according to IPU dogma, don't actually bite people but are drawn to Invisible Pink Unicorns like horseflies are to horses.
The IPU has also become a sort of mascot for atheists and other non-believers who display her image on shirts, mugs, etc.
As with the Islamic tradition of adding epithets to the names of Muslim prophets, "IPUists" generally add the epithets "Blessed Be Her Holy Hooves", "Peace Be Unto Her", or "May Her Hooves Never Be Shod". These are commonly shortened to bbhhh, pbuh, and mhhnbs.