Apple hit a market capitalization of over $620 billion this morning, breaking the record of $618.9 billion set by Microsoft back in 1999. The company is now worth over $200 billion more than the second largest company in the world, Exxon Mobile, and almost $400 billion more than the $256.7 billion Microsoft is today. It should be noted that, when adjusted for inflation, Microsoft's previous record totals around $851 billion, meaning that Apple hasn't quite usurped the title of most valuable company ever. It's also possible that Microsoft's record could have been beaten by monopolies like Standard Oil in the distant past, supposing their capitalizations were also adjusted for inflation.
Apple's valuation is a multiplication of its share price, currently just over $660 per share, and the number of outstanding shares available to investors. The company's share price has been steadily increasing as of late, as rumors of a new iPhone and a smaller version of the iPad have gained steam.
Update: In a previous version of the story we indicated that Apple had become the most valuable US company ever. However, this is not the case when the figures are adjusted for inflation.