Shares of Apple Inc. today rose $3.94, or 1.80%, on heavier than average volume of 32,647,77 shares to set a new all-time closing high of $223.02.

Apple’s previous closing high was $219.09 set on March 8, 2010. Apple’s all-time high (intraday) stands at $225.00, set during trading today. Apple’s 52-week low was $82.57, set on March 9, 2009.

At market close, Apple’s market value stands at $202.14 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 has a market cap of roughly $205.13 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) – $315.59B
2. Microsoft (MSFT) – $252.50B
3. Wal-Mart (WMT) – $205.66B
4. Apple (AAPL) – $202.14B
5. Berkshire Hathaway (BRKA) – $191.89BB

Selected companies’ current market values:
• Google (GOOG) – $177.91B
• IBM (IBM) – $163.12B
• Cisco (CSCO) – $149.61B
• Hewlett-Packard (HPQ) – $122.38B
• Intel (INTC) – $115.67B
• Disney (DIS) – $64.53B
• Amazon (AMZN) – $57.27B
• Nokia (NOK) – $52.40B
• Research In Motion (RIMM) – $40.96B
• Sony (SNE) – $37.30B
• Dell (DELL) – $27.76B
• Yahoo! (YHOO) – $23.15B
• Adobe (ADBE) – $18.41B
• Motorola (MOT) – $16.12B
• Palm (PALM) – $953.60M
• RealNetworks (RNWK) – $687.70M

AAPL quote via NASDAQ here.