I sometimes wonder what it would be like if we lived in a society where we could directly ask someone something like "What's the basis of your self esteem?" - I suspect a lot of us have a list of things that it is important for us to believe we are - popular, just, intelligent, tough, stylish, a good member of X ethnic group, on the path to being a tv star, etc. For some of us, we wear these on our sleeve - people who not only need to believe that they are X but need to believe everyone around them thinks them to be X as well. This creates problems, of course, when others do not believe it (and selects their circle of friends/acquaintences, in many cases). For others, it's enough that they believe it and they can disregard what most (or all) others think on the matter.
If one is observant enough, of course, one can see parts of this in others, but I suspect that many times, even with really close friends (maybe spouses too) one never gets the whole picture. I don't think I've ever thought to ask this of anyone I've dated or known nor has anyone ever asked it of me. I'm not sure I'd want to give an honest answer anyhow both because these kinds of things often sound arrogant or weird and having others know the honest truth of it gives a terrible vulnerability - the lines to self-esteem are disruptable in many cases.
It's interesting to think about what one can do if one finds that one's self esteem is based on things that are either unhealthy or lead one to actions that are against one's values (anorexics are an example of the former).