Facebook sometimes does this really neat thing where they show a thumbnail preview of a website you link to in a status update. It is usually the website\'s logo.
Try your site in this facebook debugger tool.
http://developers.facebook.com/tools/debug
It will tell you what is missing.Eg. below in page head
<meta property="og:image" content="[url to image]" />
<meta property="og:title" content="[page name]" />
<meta property="og:description" content="[content description]" />
There are different ways depending on how your site is built. Eg. This Wordpress plugin creates a link for each image on the page so you can chose between your logo and any other post image on the page.
Update 2017: It is now recommended to register a Facebook App ID for your site otherwise the debugger will give you an error. More tags and info
You can put this in your page's source:
<link rel="image_src" href="http://somesite.org/img/title.jpg" />