Apple (Nasdaq: AAPL), the world's most valuable technology company, continued its tear as its shares keep setting all-time records in Monday trading. Earlier, its shares hit $664.75, valuing the Cupertino, Calif., company above $621 billion for the first time, more than any other company's prior value.

In mid-afternoon, Apple shares rose $14.04 to $662.15.

Exxon Mobil Corp., No., saw its shares fall 54 cents to $87.86 in afternoon trading, lowering the Irving, Tex., energy company's value to $405.5 billion.

Apple's rival, Google (Nasdaq: GOOG), the No. 1 search engine, also saw its shares surge to a new record of $678.87, before easing back to $676.32, down 82 cents, valuing the Mountain View, Calif., company at $221.2 billion.

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