For the second time in as many years, Apple Inc. AAPL is No. 1 on Fortune Magazine‘s list of the World’s Most Admired Companies.

“It’s been a rocky year for Apple,” writes Alyssa Abkowitz. “CEO Steve Jobs’ health made headlines, and critics said Cupertino wasn’t being open enough about it. But customers remained loyal to the brand that made white ear buds cool. As much of the computer industry struggled, Apple shipped 22.7 million iPods during its first quarter (up 3 percent from last year), 2.5 million Macs (up 9 percent), and 4.4 million iPhones. No wonder Apple tops our Most Admired list for the second year in a row.” (link)

In the nine key attributes used to rank the companies, Apple got top marks (1 out of 12) for innovation, people management and quality of products/services. It got lower marks (5 out of 12) for social responsibility and global competitiveness.

Curiously, when judged by its peers (i.e. other companies in the computer industry), Apple came in No. 2 after Xerox XRX and above Hewlett-Packard HPQ .

In the broader list of most admired companies in any industry — judged by companies both inside and outside the computer field — HP came in No. 30 and Xerox didn’t make the cut.

To see the full list, click here.