Warning: Wikipedia contains spoilers.
Originally, this character was simply called Montgomery Burns, but in one episode, he yelled "You can't do this to me, I'm Charles Montgomery Burns!", which plays on a quotation from Orson Welles's Citizen Kane ("You can't do this to me, I'm Charles Foster Kane!") His catchphrase is the word "Excellent" muttered in a low, sinister voice with tented fingertips.
His age is most often mentioned as being 104 years. (Though once in the episode where he ran for governor against Mary Bailey he stated his age as 81 after Homer guessed 102; and he once had a ninetieth birthday during the series.) He has credited his longevity to Satan. He has the same blood type as Bart Simpson, double-O negative. According to tests done at the Mayo Institute, he has every single disease known to man, and survives only because they are just barely perfectly counteracting one another.
Occasional flashbacks show his early life. His family owned nuclear factories at the start of the 20th century, although back then splitting atoms was a labor intensive process done with hammers and anvils. As a privileged rich child Burns would amuse himself by injuring hapless immigrant laborers. Burns still sometimes imagines that such activity is a socially acceptable amusement for the well-to-do. He is portrayed as the prototype of an early capitalist exploiter. When he was very young, however, he lived happily with his loving, natural parents and brother George, and his teddy bear Bobo. He chose to give this up and live with a twisted billionaire, presumably (given the above information) another relative who subsequently raised him. He has since recovered the bear.
Burns graduated from Yale University in the class of 1914. He may have had an affair with Countess von Zeppelin. He apparently speaks fluent German. His mother who is now 120 years old, once dated President Taft. He served in the United States Army in World War II, seeing action in Europe under Sergeant Abraham Simpson. At the end of the war he was personally hired to transport a trillion-dollar bill that was the American Government's original contribution to the reconstruction of Europe, but this bill vanished for many years.
During the 1960s Burns operated a biological weapons laboratory until it was destroyed by peace activists including Mona Simpson.
He has occasionally run other businesses in Springfield, most notably a casino that operated for several years after Springfield legalized gambling. He co-owned the "Lil' Lisa" recycling plant. He slant-drilled for oil under Springfield Elementary School.
Burns now lives in a mansion on an immense estate called Burns Manor located at the corner of Croesus and Mammon streets in Springfield. This estate includes attack dogs, a robotic Richard Simmons, a room with a million monkeys at a million typewriters, a bottomless pit, a human chessboard (formerly a tennis court), the largest television in the free world, a Hall of Patriots commemorating his ancestors, and artefacts such as the only existing nude photo of Mark Twain and a rare first draft of the Constitution with the word "suckers" in it. His telephone number is 555-0001. His Social Security Number is 000-00-0002: he claims that FDR beat him to having the first number.
Burns has a son, Larry Burns, the product of a brief affair many years ago, but they do not get along. Bart was briefly his heir. It is not known who presently stands to inherit his wealth. (Smithers is to be buried alive in Burns' coffin).
Burn's mental state seems to vary between being fully alert and being completely delusional. He often slips into using language appropriate for the early 20th century or even the 19th century -- for example, he thinks that Prussia is still a separate country (it became part of Germany in the 1870s) and that Thailand is still called Siam, and he answers the telephone "Ahoy hoy!" (in the manner of Alexander Graham Bell before "hello" became commonplace).
The character of C. M. Burns partially is patterned after Howard Hughes (for example, wearing Kleenex boxes on his feet), with notable similarities to William Randolph Hearst (indirectly through Citizen Kane), Scrooge McDuck, and others. He bears a striking physical resemblance to Fred Olsen, (see comparison at http://www.skundberg.no/oystein/ymist/tvillinger/ ) a Norwegian shipping magnate and owner of the Timex watch brand.