Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.
- Alexander Pope
Sir Isaac Newton was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian and one of the most influential men in human history. Anything you can think of, this guy already thought it. :)
His birthday was January 4, 1643. Due to subsequent changes in the Calendar, in that era the year started later and that day of the year was Christmas Day at the time. His was a premature birth, 3 months after the death of his father. His mother remarried and abandoned him, for which he eventually threatened to burn down their house with them in it.
He attended Trinity College, Cambridge. In 1665 the college was closed because of the Black Death Pandemic. Later he returned as a Fellow of the college, and eventually became a member of the Royal Society. Late in life, after a nervous breakdown, he became a member of the Parliament of England and the Master of the Mint. As Master of the Mint, he switched England over onto the Gold Standard, and prosecuted counterfeiters. His efforts (including undercover work) resulted in the deaths by hanging, drawing and quartering, of many counterfeiters. He was knighted in 1705 by Queen Anne.
He died on March 31, 1727. He was unmarried, and he wrote that one reason to study science was because occupying his mind with great mysteries made maintaining his chastity that much easier. It's been suggested his death was related to mercury poisoning, and that a lifetime of exposure to chemicals contributed to his eccentric personality.
In 1687 he published the Philosophiæ Naturalis Principia Mathematica, one of the most influential works of science ever written. It includes his famous three Laws of Motion, and calculations of universal gravitation. One criticism at the time was that while he included calculations of gravity and orbits, he did a very spotty job of explaining what gravity actually was. In fact, some critics at the time accused him of occultism, saying that gravity was an occult or magical force.
- He invented the reflecting telescope.
- He determined that white light contains all colors, and was the first to correctly understand how a prism works. He was the first person to realize that color is not a property emitted by objects, but rather the result of their interaction with already-colored light.
- He studied how his own eyes worked by sticking a bodkin (a type of large needle) between his eyeball and the eye-socket, and noting the visual aberrations this contact with the optic nerve created.
- He's one of the two inventors of calculus.
- He himself claimed to figure out gravity when an apple fell at the tree he was studying under. Prior to his work on the topic, even great minds like Galileo assumed different physical laws described movement near the earth than described movement of heavenly bodies. Newton unified it all under one set of laws.
Newton's contributions to science are what made him famous, but that should not be misunderstood to colorize him as a man of only the empirical and scientific world. In the words of John Maynard Keynes, "Newton was not the first of the age of reason, he was the last of the magicians."
His study of Chemistry lead him to decades of research into Alchemy. He sought the Philosopher's Stone and the Elixir of Life, and believed the secrets were encoded in mythology. For a good example, see The Net (substance). It's worth noting that Alchemy was outlawed in England at the time - had he been exposed, the punishment was public hanging from a gilded scaffold.  Due to the dangerous and scandalous nature of Alchemy, Newton hid his efforts. On the backs of two pages of his manuscript "Of Natures Obvious Laws & Processes In Vegetation", he wrote in coded Latin, backwards and upside down, research he'd done into Vegetation of Metal, and his theory that gaseous metals wandered the earth and created life. 
In general, Newton believed that ancient man held much wisdom and knowledge that had been lost. His personal library included 169 books on alchemy, plus related fields such as occultism, tarot, and heiroglyphs, in addition to scientific and theological works. He owned 30 bibles. He was very fascinated with Sacred Geometry and especially the Temple of Solomon, which he believed was built with Divine Guidance.
Many of Newton's beliefs and theories were heretical, or at least controversial. He was an antitrinitarian, and believed firmly that while Jesus Christ was the son of God, Christ was not himself God. Newton felt that belief in the holy trinity was a flagrant violation of the First of the Ten Commandments. Further, much as he found alchemy coded into the greek myths, he found prophetic codes hidden in the bible. Newton himself calculated (from these scriptural codes) that the end of the world would happen in the year 2060.
His 87,000 word The Chronology of Ancient Kingdoms traced ancient civilizations to Atlantis, and his Original of Monarchies traces bloodlines of contemporary kings back to the biblical figure of Noah.
Game and Story Use
- Newton spent decades studying Alchemy and trying to turn lead to gold and make a potion of immortality. He lived into his 80s (in an era where that was rare), and eventually became Master of the Mint. Perhaps there's something to this Alchemy business afterall?
- As a historical figure, Newton can be an inspiration / hero / rolemodel to skeptical scientists and occult aspirants alike.
- Newton's belief in coded mythology and the greatness of ancient civilizations could bring him into contact with Ancient Astronauts.
- For more ideas see Julius Beethoven Da Vinci and Beethoven Was An Alien Spy - either could be easily adapted to Newton.
- There is an obvious … but not complete … analogy to John Dee there if you want it.