Kevin Ross of Digg confirmed that copy&paste ability would come with the new iPhone software (version 3.0) during the Diggnation event in SXSW in Austin, Texas.
Kevin described the functionality, such that upon double tapping, a magnifying glass would appear like it did before, but there would be two quotes on each side. By pulling the quotes, users would be able to select text. After selecting, it will be possible to cut or copy the selected text.
The video below is the moment Kevin confirms this functionality. Warning, strong language.