A WebmasterWorld thread reports that the only way to request reinclusion into the Google index is to admit you violated Google's terms of service. If your site has been removed from the Google index, you can then file a reinclusion request with Google within Google Webmaster Central.
But as this WebmasterWorld member noted, you must first admit that you were guilty.
I have gone to Google’s reinclusion request form to look into submitting a reinclusion request for the site. However, to submit such a request, you MUST agree to a declaration that the site has been spamming (you must agree to: “I believe this site has violated Google's quality guidelines in the past.")
Again, you must check off a box where you say, "I believe this site has violated Google's quality guidelines in the past."
If you do not believe the site has violated Google's quality guidelines, then what is an honest person to do?
Senior member, BillyS feels that "it's a rather arrogant way to approach this problem." But jomaxx says something pretty smart, "but if absolutely nothing has been identified or changed is a reinclusion request going to do any good?"
There are times where one takes over a domain that may have done something against Google's guidelines. In that case, you can easily say, yes - it is possible, the previous owner, did things that were wrong. But if not?
Forum discussion at WebmasterWorld.