I feel that the companies that are most admired are those that impact their respective communities the most and those that have a positive impact on peoples day to day lives.
The first, and best, company that comes to mind is Starbucks. Starbucks was built off of the thought that they could provide a "second home" where people of the community could relax, converse, and enjoy a great cup of coffee. They have something like 22 repeated visits by customers a month, that is amazing. All of the employees love working there as well, which directly effect the mood of each store. All of these things makes the public admire the company.
I think the reason most companies are admired is mostly due to innovation and company culture. Google, Apple, Zappos, all come to mind.
As for companies I admire, It would have to be those that remain private, dont go for angel or VC capital.
The most admirable company I can think of, and most admirable person is the founder of wikipedia. To give up being a potential billionare is something I know would be hard for anyone to do. It just shows you, its not about the $$$, but about the game, recognition, and creating something that you love.
I admire companies for similar reasons to why I may admire certain individuals: the entity in question has worked hard and survived multiple challenges, over enough time to not be luck, through creative problem solving all while maintaining a positive behavior.
Now, of course, there is a big personal dimension to what constitutes "positive behavior", so that's where it becomes totally subjective. For me, what I admire is not power, but rather "disruption" and "enablement". Who's changed the game? Who's maintained a social conscience while being successful, challenging the idea that business is cut-throat? Basically, high performance with high integrity, to paraphrase Heineman.
Off the top of my head, some companies I would personally list:
I would not look at the companies for an answer to this, rather to the people who attribute value. As with all other things, different people value different things.
So, we see groupies/fanboys/admirers/proponents/evangelists for many companies and for many different reasons.
If a company is able to align itself with some group's interest and priorities and culture it is likely to have admirers.