In the essay, Rand is quoted as making the following two statements:
The worst evil that you can do, psychologically, is to laugh at yourself. That means spitting in your own face.
--Ayn Rand Answers, p.141
One of Ellsworth Toohey's most evil lines in The Fountainhead is his advice that 'we must be able to laugh at everything, particularly at ourselves.'
--The Art of Fiction, p.166
Upon first reading these, I found myself disagreeing strongly with both of them. My opinion is and has been that the ability to laugh at oneself demonstrates health and good-naturedness. In thinking about it, and reading through the essay and a few more of Rand's statements on humor, I find that these views are actually very easily reconcilable with my own. Consider this statement by Rand:
Humor is the denial of metaphysical importance to that which you laugh at.
--Ayn Rand Answers, p.140
In the essay, Robert Mayhew distinguishes between benevolent and malicious humor. Benevolent humor is basically humor aimed at objects which deserve scorn and ridicule, while malicious humor is aimed at objects which deserve respect and reverence. Thus, benevolent humor belittles the metaphysical importance of bad things, while malevolent humor belittles the importance of good things. Now, humor which is aimed at one's own achievements, or more generally one's own positive values, is obviously malicious humor. Laughing at oneself in the sense of laughing at these things is indeed bad. However, in thinking about it, that is not at all what I picture when I think of 'the ability to laugh at oneself.'
Consider someone who slips and falls, or misspeaks in some absurd way, or makes an obvious error in a presentation. In all of these situations, I am inclined to think of the person who can 'laugh it off' as good-natured. I would contrast this with the image of the person who, when something like this happens, blusters and attempts to 'save face.' Obviously, this second person is primarily concerned with others' impressions of him rather than the actual error or accident. Such second-handedness is clearly not an appropriate attitude.
But what is the first individual doing? First of all, he is acknowledging the reality of the accident or mistake. Furthermore, he is (in Rand's characterization) belittling its importance by laughing at it. Self-deprecating humor, in this case, is not aimed at ones values, but rather at one's mistakes. This form of humor is indicative of genuine self-esteem; the person in question is acknowledging the reality of his own thoughts and actions (an essential first step for genuine self-esteem) and is able to casually dismiss errors with a laugh. There is no attempt to pretend for the sake of others' opinions that the error was not made; rather, it is acknowledged and then moved on from.
In my experience, the majority of instances of self-deprecating humor fall into this latter category of laughing off a mistake. Thus, while it is true that actually cutting oneself down with humor also undoubtedly occurs, the everyday understanding of 'laughing at oneself,' (at least what I think is the prevalent understanding of it) is a healthy practice, one which should be celebrated.