>You have the right to exclude your listings using the robots.txt file. It's your choice whether or not to allow Y! or GG to show your results.
Actually, that is exactly the opposite to how copyright works.
When you create something, you own copyright (the right to copy) in that creation. No-one may make a copy of your creation without your consent. Period!
Therefor, theoretically, no one can copy your web pages, including code, images and other component parts, without your permission. Of course, that is not the way browsing works in that a user must download and copy said code/parts to their computer for it to be rendered by their browser.
However, taking said code/parts and storing them for further manipulation to create a new object out of those code/parts is in violation of the core essence of copyright laws.
Therefor, again theoretically, for a search engine or directory to list your site using content from your site without your permission is a breach of copyright.
One could argue that submitting to a directory includes a tacit agreement to use material from your site in the listing. This may or may not be covered by the conditions of particular directories. But even then, directories, myself included, will often use a description from the page in the listing without obtaining permission.
on the other hand, search engines in general, and other spidering entities, would like to reverse copyright laws by saying "we will take anything we want unless you tell us not to." (Even then, they may not obey instruction given in the robots.txt file and may require more drastic action to prohibit them from spidering.) That is like saying "I am going to rob your bank unless you tell me not to, regardless of the fact that robbing banks is against the law."
As I say, this is all theoretical, as, in real life, we all know the opposite is the accepted practice.
There is a fine line though between presenting a portion of a page for the purpose of assisting the user in deciding the usefulness of said listing to his query, and using the stored version of the page, or portion/s thereof, for the creation of a new work or works for which the "new creator" cannot hold copyright simply because the "new creator" does not hold copyright in the original component parts nor has obtained permission to use said component parts from the original copyright owners.
It is indeed a tangled web.