Apple Computer was founded by Steve Jobs and Steve Wozniak (and Mike Markkula) on April 1, 1976 around the Apple I computer constructed by Wozniak. (the other guy later dropped out, as Jobs wanted to take big loans). Jobs even gave up his VW bus to found Apple (and Woz sold a programmable calculator). His work was partly inspired by discussions in the Homebrew Computer Club.
The name. There are two legends about the name and logo of Apple Computer. It may have been inspired by the mathematician Alan Turing who opened up the field of computer research notably with the enigma machine and his ficitonal Turing machine. Turing committed suicide by biting in to a poisoned apple, hence the logo. The other legend is that the founders of what would be Apple were sitting around the table. One of them was eating an apple and told the others that if they could not come up with a name, they might as well name the company after this apple. Some people also claim that Apple was named after Apple Records, the Beatles' recording company, and even other people claim that it was named after the apple that supposedly fell on Newton's head and made him discover the laws of gravity. Apple Records later sued Apple Computers for the name, and they agreed that Apple Computers could keep the name as long as they kept out of the musics business. Of course, Apple Computers eventually introduced quite advanced sound capabilities into their Macintosh Computers, which Apple Records didn't really like. Apple Computers therefore introduced a new system sound (a "beep") called "Sosumi" - "so sue me".
Soon after the Apple I followed by the more advanced Apple II family and Apple III (which was a disaster). After visiting XEROX Parc (and letting XEROX invest $1 million into Apple which later turned to around $17 million), Jobs recognised that the future was graphics and Apple started to experiment with more advanced graphical user interfaces (GUI), resulting in the Apple Lisa computer (a commercial failure because it was too expensive), and finally, in 1984, the myth-making launch of the Apple Macintosh computer. Actually, both projects were developed simultaneously; after dumping Lisa, the Mac could get the attention it deserved.
Products from Apple also include operating systems such as ProDOS and Mac OS, networking products such as AppleTalk and multimedia program QuickTime. Discontinued products include the Apple Cube and Apple Newton handheld computer.
It is thought by many that Apple's main innovations were done after their famous visit to Xerox Parc, even though in reality work on the Macintosh project started long before that, and the Macintosh operating system ended up working and looking quite different from the programs at Parc. They added the menubar, overlapping windows and icons representing objects instead of actions, for instance. The XEROX guys also sued Apple after 10 or so years of the first usage of the GUI (To do: result of lawsuit).
Recently, Apple has introduced Mac OS X, a new version of their operating system that finally marries the stability of Unix with the ease-of-use of the Macintosh Interface in an OS targeted at professionals and consumers alike.