Longcat is a picture of a white cat being held up so as to stand on its back feet, showing off its unusually long body.
Longcat became a fairly popular meme on /b/, and predictably has been photoshopped to hell and back by /b/tards. At first, it was known as Patriot Cat or "Pat Cat" and simply photoshopped in front of the World Trade Center Towers, protecting them from attacking airplanes. It was somehow forgotten and then dug up again with the now common name. Posts of Longcat are often accompanied by the text "Longcat is loooooong". The phrase is frequently altered not only for other cat memes ("Speedycat is speeeeeedy", etc), but also for general use. For example, a lame macro or image edit might be replied to with "Shitty Photoshop is shitty". Longcat's real name is Nobiiru, which is Japanese for "Stretch".
A graphic of Longcat was used as 4chan's donation meter in 2005, as part of DONATE OR DIE. In most boards, Longcat gave an accurate representaion of the donation level, but in /b/ a variety of random Longcat graphics (such as an upside down Longcat, a black Longcat, and Longcat's body extending beyond the top of the screen) were displayed instead. Most modern Longcat images now feature the cartoon donation Longcat rather than the original.
It's worth noting that the use of Longcat was pioneered in 1969 in an insert animation by Terry Gilliam for the first season of Monthy Python's Flying Circus.
Longcat's arch rival, a similarly long cat that is black rather than white. Its name is "Longcat" spelled backwards. Due to its color, Tacgnol is also known by names such as Blongcat, Nigra Longcat and Nega Longcat. Some argue that Tacgnol and Longcat are in fact one and the same, the begining and the end. Tacgnol was needed to destroy /b/ so that it may be reborn again.
Tacgnol claims to have been created by Raptor Jesus and to be the true messiah of /b/. His eyes glow an ethereal green color and he is held up by woman rather then a man.
A human personification similar to Longcat. Long-chan has a legless, infinitely long body reaching far above the clouds, a body which she tends to knot and curve into various figures on occasion. Despite not having a crotch per se, this doesn't stop her from self-pleasuring, as she can freely summon a vagina within arm's reach, approximately where one would find the crotch on a normal girl. She is often the object of obsessive love from Anonymous and ends up on the receiving end of various stalker letters that attempt to learn every possible detail about her sexuality. Many /b/tards have attributed her the power of instantly summoning a flood of sage replies whenever she is posted in a thread.