In an earlier post I took you through some of my favorite desktop F/LOSS projects, and I've blathered on about the Flock browser separately. If you really want to embrace the social web, though, you should bring some of it home to your organization. Hosting your own blogs is a start, be it a stream of current news and events or as a discussion or soapbox for your CEO or media relations people. Wikis are powerful collaborative tools for both your internal staff projects as well as collaborative, evolving documents you work on with your constituents. Wikipedia runs on open source software called MediaWiki, which you can download for free and get running in under an hour (less on Linux systems, it can be a bit tricky with Windows servers). There are more open source blog options than I'd care to even begin to list, and which one you chose in the end will depend on how you plan to use it.
Before jumping head on and installing all these pieces individually (and without some customization, requiring separate logins for each separate piece), you should also consider a more fundamental change in your website -- moving to a Content Management System, or CMS. There are two very popular F/LOSS CMS systems out there today, Joomla and Drupal. Drupal constantly amazes me with its ease of use, but Joomla seems to be easier to conform to your existing web design, whereas Drupal is hard-headed about its concept-based layout. I've seen many amazing Drupal sites, and since they're both a breeze to get running with install wizards that will have you playing in the CMS in seconds (really), why not try both? If you don't want to install both, you can also look at OpenSourceCMS.com, which runs these and many many more, giving anyone access to go in and fool around (they automatically reset every hour).
These CMS systems can integrate many popular tools, and/or have versions of them built in, allowing you to have a single-sign-on for all of your various web 2.0 applications. Drupal and Joomla especially are designed with sharing and integration in mind, so they naturally work well with other web 2.0 sites by sending out and importing RSS feeds, plugging in at the API level with Google Maps, Flickr, and so on, often by downloading freely available plugin tools, created by a global team of volunteers working together to share their tools. As an extra bonus, most of the geek types working on these systems are also obsessed by following best practices and web standards, giving you cross-browser and cross-platform compatibility, even with mobile/cell phone browsers with a little work, and accessibility built in.
CMS systems also empower your staff to edit their own web pages instead of having to go through IT for each forgotten comma. They include easy to use editors, ranging from simple text to foll-on WYSIWYG interfaces. The degree of design freedom varies among the different CMSes, but remember that more freedom risks less cohesiveness in the overall site design.
Here's a few sites done using Joomla and/or Drupal, to give you a taste of the power built in to the systems -- these aren't hodgepodges of tinkerer code, but enterprise-class systems:
Of course, you can shell out the big bucks for custom software or commercial CMS tools, but you run the risk of that company going under and taking their software with them. With FLOSS, you will always have the source available -- this means never getting locked out or left behind, and always being able to go your own way and hire a different firm to modify the code, but you don't have one big company to call to add a new feature in (kinda). FLOSS is created by a global network of interested volunteers and requires additions to also be freely shared, so you can often find other people working on the same problems you might be encountering.
Remember, It's not good because it's free, it's free because it's good!