The Ancient Mystic Order of the Rosy Cross (AMORC), aka the Great White Brotherhood, had their origins in the Egyptian mystery schools, which were originally primarily concerned with agriculture and natural sciences, and held classes in out of the way places like grottoes, on a word-of-mouth basis only. They were credited with coming up with the notion that all that exists is motion, and they symbolized this with a rattle, or sistrum (being as the beads inside, when shaken, were in motion), which was later misinterpreted as being meant to scare away spirits. 'Course, it took until this decade for Western science to get back to this idea, due to factors I'll mention later. Their first real organization came during Egypt's 18th Dynasty, when pharaoh Ahmose I (1587-1557 BCE) started holding these classes in his private chambers, being a pretty sharp scientist himself. The GWB wasn't a formal order until around 1500 BCE, when it was organized by Thutmose III, who outlined most of its rules & regulations.
Later on, Amenhotep IV, being a pharaoh and thus part of the GWB by default, came up with the concept of monotheism, in the sense that he instituted the worship of the sun as a symbol of 'God' rather than the sun being a god in and of itself. He also changed his name to Akhnaton (meaning 'pious to Aton,' the sun god) and built the GWB a cross-shaped temple at El Amarna, which was reputedly the first monastery. He also came up with the rose/cross symbolism and the ankh, or crux ansata, which are blatantly sexual/generative symbols. However, the Egyptians in general went right back to polytheism when he died in 1350 BCE.
Anyway, the order stuck around. A bunch of Greeks went to Chaldea & Egypt to learn about it, but the Egyptians played it cagey, seeing as said Greeks didn't have a clue. They didn't induct any of them for that reason. The Greeks then went back to Greece and made up a bunch of stuff (including Aristotelian mechanics) based on a fairly radical misunderstanding of the GWB's ideas. This more or less completely screwed up physics for centuries.
Around the time of Ramses II, the Egyptian government and people started getting paranoid about the GWB, being as they knew entirely too much and held too much power. At this point, the Egyptian government was starting to decline pretty badly, so one of the order (Hermes, aka Hermes Trismegistus, or thrice-blessed, who was the Head of the order for a while) finally committed most of their info to writing on a bunch of tablets and books, in code so nobody but GWB could understand them. The writings were hidden, and not found again until about 400 AD.
Later on, around 1200 BCE, a bunch of GWB personnel were sent out to start other Lodges, being as Egypt was probably going to be trashed. It was around this time that they came up with their AMRA policy, which was to let people come from other places, get trained by the Egyptians, then go back and start Lodges at home.
Solomon (yeah, that one) got to El Amarna around 1000 BCE, studied with the GWB for a while, then took off for Bubastis before he'd finished his studies. From there he traveled around Egypt for a while, teaching and advising, and during this period founded Freemasonry based on a mixture of GWB monotheism and Egyptian polytheism. He was credited with coming up with the Father/Holy Ghost idea, as he conceived of the sun as God's body, or active principle (unlike the GWB, who thought of it as a symbol). He later went to Palestine and had his Biblical adventures, eventually building his Temple, which was a copy of the one at El Amarna, minus the side structures that made it cross-shaped. He was helped with this by two Egyptian architects, Hu-Ramabi and Hiram Abif. Freemasonry spread from there.
Back in Egypt, the GWB was kind of irritated with Solomon, as he never bothered to affiliate with them and ripped off and corrupted their teachings, but they more or less left him alone, as the Greeks were starting to come back and they were a bit busy dealing with them. Pythagoras came from this wave of Greeks, and was inducted into the GWB. He then went and founded an Italian Lodge at Crotono (or Krotono).
As the years went by, the GWB spread out, and a lot of scholars from various places came down to Egypt to study with them, including quite a few Greek philosophers (Plato for one). They realized that the GWB was more or less the only source of reasonably accurate information about the way the world worked at the time. Their teachings were misunderstood and misinterpreted on a regular basis, though. The Order kept a huge amount of information secret and available only to its members. One of these was Moses, who adapted the monotheism he learned from the Order to his people's myth-system and went from there.
The GWB periodically sends out representatives whenever mysticism seems to be declining to mix their doctrines into pop philosophy. Plotinus did this around 200-something AD by mixing GWB principles with Platonism, producing Neo-Platonism. He also picked up the idea of good and evil as a single force in Persia, and incorporated it into GWB philosophy.
Around the time Iehoshua of Nazareth (aka Jesus) was born, the GWB was operating in and around Heliopolis and Mount Carmel. They started preparing for the reincarnation of their previous 'Avatar,' Zoroaster. Iehoshua turned out to be said reincarnation. When he died, they started the Catholic Church loosely based on his teachings, with a liberal dose of Egyptian mysticism thrown in. They never bothered to fully control it, and it evolved into the more or less independent organization we know today. A couple of hundred years later they moved their HQ to an isolated part of Tibet.
During the time in which the Christian (aka Christine, Pauline, Catholic, etc.) church went through a lot of trouble, the GWB formed a militant branch known as the Militia Crucifera Evangelica (MCE) dedicated to protecting the Egyptian cross symbolism against misuse. This inspired a lot of other similar organizations (the Templars, Hospitalers, etc.). The MCE is still around; they had their first American meeting in 1940.
Over the years a lot of famous people have been involved with the GWB's operations; past prominent GWB members include Charlemagne, Albertus Magnus, Thomas Aquinas, Dante Alighieri, Sir Francis Bacon, Rene Descartes, Isaac Newton, Count Alessandro Cagliostro, Ben Franklin, etc.
A couple of hundred years BCE, the GWB started their 108-year cycles of inactivity and activity. They operate publicly for 108 years, then pretend they've been suppressed, operate underground for another 108 years, then go public again, pretending to have found their ancient teachings in the tomb of someone named C.R-C. (simply meaning the Christus of the Rosy Cross). They then appear to be a brand new order in the eyes of the public so nobody gets too paranoid. This also provides a way to tell easily if a 'Rosicrucian order' is full of it; if they claim to have been founded in Germany by a 'Christian Rosenkreuz', or be a descendant of the 'original lodge' in Germany, they're either lying or misled.
Later on in England, quite a few Freemasons got interested in the old GWB teachings again and started a Freemasonic 'Rosicrucian' society, known as the Societas Rosicruciana in Anglia (SRIA) based on some records one of their members found in a library, apparently from one of the bogus German 'Rosicrucian' orders. This has evidently caused a lot of people to confuse GWB-style 'Rosicrucianism' with Freemasonry in practice.
And that's Rosicrucianism in a nutshell.