I have an online service (website security) and a blog where I write about prevalent hacker attacks and about how to detect break-ins and clean up websites.
Every now and then, big-name sites and blogs of well-known companies refer to my blog posts. Sometimes journalists ask me questions and then quote my words in their articles. Sometimes they even mention my service (since I mention it in my blog posts).
However, all stories are not about me or my service so I can't put a "Featured on NYTimes.com " or "Recommended by CNet " banner on my site. Still I feel that I somehow should benefit from those references. At this point the only thing I do is tweet about articles on big-name sites that refer to my posts, but as long as I'm not Robert Scoble this hardly makes any difference.
By big-name sites I mean: (The New York Times, Washington Post,Guardian.co.uk, TheRegister.co.uk, CNet, PCWorld, ComputerWorld, CIO.com, Sophos, IBM, Google, etc.)
I would add a prominently-placed section titled "XXXX in the news" to your page and put links to mentions/citations/quotes of you in there. You should make this a static section so it never scrolls past. Make sure you highlight the publication in each entry (since that is what you want people to notice right away). Something like "NYTimes - 1/10/09 - Article title" for each linked article.
You could just put a scrollable section on the side of your site where people can see where you were mentioned. As the list gets longer you may want to have where they can select the type of media, also, and, as gmagana mentioned, includes links to the story, and perhaps also link to your blog post that was the reference, as it may not be obvious to the reader, and this double-link could be very useful, to see what led to others referring to you.
I think the "Recommended by CNet" comes with a slightly lofty price tag. If you are mentioned, feel absolutely free to mention that you were mentioned in any way you see fit. Just do not imply endorsed unless you have a specific arrangement (or endorsement).
You can and should capitalize on what you told them.. after all, they do.