If your site is mentioned on another popular related site, it's a happy day indeed as it can drive a lot of traffic and help with your search engine rankings.
.. unless ..
They don't actually link to you.
It's not uncommon for this to happen, particularly on major media sites - they may just mention the name of your company or business. People can still find you of course, but whether they'll go to the trouble to even copy and paste the domain name (if even that is mentioned) into a browser address bar is another story.
I'm not 100% certain if Google apportions some link love if, for example, just the domain name is mentioned without any link like so:
It certainly won't if the business name is presented in this way.. "Joe Bloggs from Example said.."
It's certainly a nice hat tip to get recognition, something you can perhaps mention on your press pages and such, but you want and need that link - for the convenience of their readers, and is it could help you along in your search engine rankings.
Why sites don't link
The reasons that the other site may not have linked to yours:
The last point is probably the most common these days and it's my understanding that is simply not true.
Google Engineer Matt Cutts addressed this quite some time ago in a comment thread accompanying his article on the topic of "PageRank sculpting" - a subject I'm not going to delve into here, only to highlight the relevant comment from Matt that stated:
"In the same way that Google trusts sites less when they link to spammy sites or bad neighborhoods, parts of our system encourage links to good sites."
So unless your site is a "bad neighborhood", there's really nothing for the other site to fear - they may even benefit as it's a case of relevant content referencing other relevant content; content that was good enough for a mention.
The other site losing visitors shouldn't really be a concern to them either; particularly if the link opens in a new tab. By not offering a link, I think there is a greater chance that they will lose readers, particularly those who then go to Google to try and find your site.
How to get that link
Ask. But ask carefully and respectfully.
I think it is worthwhile following up about a link in these situations; but you also don't want to appear ungrateful or demanding in pursuing that goal. The other site is really under no obligation to create a link to yours. If you go about it to aggressively, you may kiss goodbye any possibility of further mentions too.
Here's some suggested text you may wish to try using in an email to the other site.
Depending on the circumstances, you could also mention the search engine ranking myth, but that may be better left until you (hopefully) get a reply where that concern is stated:
Example starts ----
<INSERT LINK TO YOUR SITE>
Example ends ----
While it doesn't go into all the details of why they should link or how; as you don't know their reason for not linking, it might be something better addressed if the other site does give a reason rather than just assuming or providing a lengthy message covering all scenarios that they may simply not have the time or inclination to read. If they do respond with a specific concern, some of the information mentioned earlier on in the article may help.
By the way, don't push your luck by asking for specific anchor text - that might be stretching the new friendship just a little. Be grateful if you can just get a link and don't look a gift link in the mouth :).
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