#1 - No: The Case of Daniel Brandt
When veteran activist Daniel Brandt objected to his entry, he found himself in a new and frenetic part of the game. Brandt had earned the hostility of the game players by attacking one of their favorite sites, Google.
(The busiest Wikipedia players are also supporters of a predictable range of techno utopian causes, for example blogs and 'Creative Commons', which are defended with a religious zeal.)
The "WP:CIV" rule was suspended, Brandt was ejected, and the Wikipedia "editors" lined up to mock him for his impertinence.
"Let's all point and laugh!" wrote one, 'Ta Bu Shi Da Yu'.
"Poor baby" wrote 'Superm401'.
"Whiny and baseless," added 'Linuxbeak'. "He can cry about this until the cows come home".
(Brandt was inspired to start a site, 'Wikipedia Watch', where he recounts the experience. He says he simply wished to remove the entry, but the request was declined by Jimmy Wales).
From this example, we can conclude that you can't edit your own entry if you are not a Wikipedia fan, or display any criticism of the project.
#2 - Maybe: The Case of Jimmy Wales
The rules are rather different if you're closely involved in Wikipedia itself. Jimmy Wales has made many edits to his own entry without falling foul of the rules he helped devise. More than once he has removed a credit to Wikipedia co-founder Larry Sanger. Again, here and here.]
Wales also assiduously removes explicit use of the word 'pornography', and even 'erotica' in reference to his porn operation Bomis.com, for which he prefers the term "search portal".
Last week former MTV host Adam Curry was caught making similar edits to the history of podcasting.
Wales signs one of his own edits with the instruction -
"Please do not change it back without consulting with me personally."
From this example, we can conclude that you can edit your Wikipedia entry - if you are a co-founder of the Wikipedia project.