Shares of Apple Inc. today rose $1.82, or 0.82%, on volume of 20,428,109 shares to set a new all-time closing high of $224.84.

Apple’s previous closing high was $223.02 set yesterday, March 9, 2010. Apple’s all-time high (intraday) stands at $225.48, set during trading today. Apple’s 52-week low was $84.36, set on March 10, 2009.

At market close, Apple’s market value stands at $203.88 billion since financial sites all use the latest published share count for Apple: 906.8 million shares outstanding as of January 15. However, Apple’s actual diluted share count, as per its latest 10-Q, was 919.783 million shares, which means that the company actually has a market cap of $206.80 billion. For the lists below, we’ll use what the financial sites use.

Apple went public on December 12, 1980 and closed with a market cap of $1.431 billion. Apple’s all-time low market value was $630.9 million on July 8, 1982.

The top five U.S. publicly-traded companies:
1. Exxon Mobil (XOM) – $317.36B
2. Microsoft (MSFT) – $254.08B
3. Wal-Mart (WMT) – $204.06B
4. Apple (AAPL) – $203.88B
5. Berkshire Hathaway (BRKA) – $203.29B

Selected companies’ current market values:
• Google (GOOG) – $183.30B
• IBM (IBM) – $163.18B
• Cisco (CSCO) – $148.13B
• Hewlett-Packard (HPQ) – $122.10B
• Intel (INTC) – $117.05B
• Disney (DIS) – $64.64B
• Amazon (AMZN) – $58.02B
• Nokia (NOK) – $53.99B
• Research In Motion (RIMM) – $41.81B
• Sony (SNE) – $37.78B
• Dell (DELL) – $28.00B
• Yahoo! (YHOO) – $23.51B
• Adobe (ADBE) – $18.42B
• Motorola (MOT) – $16.44B
• Palm (PALM) – $956.96M
• RealNetworks (RNWK) – $717.36M

AAPL quote via NASDAQ here.