But there are some other things you can add to your site to make it more Social media friendly:
Open Graph Tags
Open Graph tags are tags that you add to the <head> of your website to describe the entity your page represents, whether it is a band, restaurant, blog, or something else.
If you use Open Graph tags, the following six are required:
og:title - The title of the entity.
og:type - The type of entity. You must select a type from the list of Open Graph types.
og:image - The URL to an image that represents the entity. Images must be at least 50 pixels by 50 pixels. Square images work best, but you are allowed to use images up to three times as wide as they are tall.
og:url - The canonical, permanent URL of the page representing the entity. When you use Open Graph tags, the Like button posts a link to the og:url instead of the URL in the Like button code.
og:site_name - A human-readable name for your site, e.g., "IMDb".
fb:admins or fb:app_id - A comma-separated list of either the Facebook IDs of page administrators or a Facebook Platform application ID. At a minimum, include only your own Facebook ID.
More information on Open Graph tags and details on Administering your page can be found on the Open Graph protocol documentation.
Actually, if you've already tried linking that page on Facebook BEFORE adding the "image_src" link, Facebook will keep using the old cached copy and not even see your changes. Try modifying the URL by removing or adding the 'www', or duplicate your page to test it.
I know this question is old, but I recently dealt with the exact same problem and went round and round on it for a couple weeks. Multiple searches on Google turned up a lot of useful information, but most of it was focused on Open Graph tags, which I wasn't interested in using. Turns out my site had multiple issues, but here are some of the basics.
As EightyEight said, make sure your HTML is valid - and the same goes for your javascript and server-side code (PHP, ASP, etc.). I had a small PHP error in a piece of code that was executing as a separate call to the server from the main page. Due to a number of bizarre coincidences, that code was generating a 500 error - but ONLY for IE6 and strict parsing engines like the W3C validator and the Facebook page crawler. The problem didn't appear in modern browsers (Chrome 4, FF 3.5, IE 8, etc) so I didn't see it right away, but older/stricter clients were showing the 500 every time and that was the main reason FB wasn't crawling our page (when everything else seemed to be correct).
Regarding Randy's response, he's correct that Facebook will keep an old cached copy of your page long after you've updated it. FB claims it's only held for 24 hours, but I experienced much longer times than that. FORTUNATELY, FB has released their "URL Linter" tool that will show you a preview of how your page will appear when being shared on FB, and it will force FB to instantly update its cache of your page. This was a lifesaving tool. You can find it at http://developers.facebook.com/tools/lint/
Regarding the URL Linter tool, be aware that each variation of a URL is cached separately on Facebook, so "www.example.com" is not the same as "example.com". Also, unique capitalization is stored as well, so "ExampleOne.com" is not the same as "exampleone.com". (This led to a lot of confusion between my client and myself when it appeared to me that the cache had been updated just fine and the client claimed they weren't seeing the updates. Turns out I was looking at exampleone.com and had used Linter to update the cache, but they were looking at exampleOne.com which I hadn't submitted to Linter. As a result, I ended up submitting quite a few variations of the URL to Linter just to cover the bases.)
WyrdNEXUS's advice to use the image_src link tag is spot-on. This allows you to be sure that FB is scraping the best possible image for your page. There are some varying guidelines out there about what specs the image file should have, but I've successfully used a 128px square image and have seen a 130x97 image make it through as well. Here is Facebook's official documentation from http://developers.facebook.com/docs/reference/plugins/like/:
Images must be at least 50 pixels by 50 pixels. Square images work best, but you are allowed to use images up to three times as wide as they are tall.
Obviously, FB will resize a large image for you, but you'll almost always get better results if you resize it yourself beforehand.
Regarding Mike Cooper's link to the eHow article, avoid using step #1 in that article. It was valid advice when the article was written and when Mike posted the link, but it's now better to use the URL Linter tool for previewing how your page will appear when being shared. By using Linter, you won't cause FB to cache a (potentially) bad copy of the page before you get a chance to tweak it.
Old question but recently I seemed to be running into same issue with thumbnail images from my link not showing in status updates on Facebook. I post for many clients and this is relatively new.
FB doesn't seem to like long URLs anymore — if you use a URL shortener such as goo.gl or bitly.com, the thumbnail from your link/post will appear in your FB update.