Search engines like google and yahoo routinely cache snapshots of websites, presumably as an archival aid should the source site be offline. Nothing wrong with this in principle because (a) the website owner can opt out by adding directives like <meta name="robots" content="noarchive"> to their source pages, and (b) the snapshot is presented in its entirety, including copyright information.
From omgili's FAQ:
How does Omgili benefit me as a forum/board owner?
Results from Omgili draw traffic to your board. You can also utilize Omgili to add customized search for your board, thus save valuable server resources and give your users fast and reliable results.
I'm skeptical such an aggregator will draw traffic. By excerpting all forum text and presenting it in their "preview" window (example: "This is a complete preview of the discussion as it was indexed by Omgili crawlers."), omgili users are more likely to stay on that site rather than following the link to the source site.
Finally, to my question: Is there a tangible benefit to website owners that allow search engine archiving? I can't think of any...