It was nip and tuck for more than three months, from that day in early August, when Apple (AAPL) first overtook Exxon Mobil (XOM), to mid November, when Exxon finally pulled away.

At one point in late September, Apple’s market cap (share price times number of outstanding shares) was nearly $36 billion more than Exxon’s.

But though Apple’s shares ended the year having gained more than Exxon’s (25.1% to 15.5%), it was not enough to overtake Exxon’s initial lead. Exxon finished 2011 $30 billion ahead of Apple.

The fact is, the world can live without iPhones and iPads. It still can’t get along without oil.