Similar to Firefox, actually identically to Firefox, Thunderbird supports add-ons that extend the functionality of the software. In fact, many Firefox extensions work here, too, such as AdBlocker. The extension developer just marks his work as compatible with Thunderbird, and bing, you can use it. One clever add-in is Thunderbrowse, which lets you open a Web page link right in Thunderbird, rather than having to open a browser. Of course, if you're using webmail, that's not an issue.
One area of weakness for Thunderbird is its lack of built-in calendaring. Even free webmail clients like Yahoo Mail, Hotmail, and Gmail include calendars linked to the inbox. Mozilla has calendaring projects Lightning and Sunbird, which look promising but are not yet officially released (they're at version 0.9). Lighting is a plug in and Sunbird a standalone client, so the former makes more sense for Thunderbird users. Another complaint is that the Web-based Help isn't well organized and is all about version 2 at this point—even when you click from version 3.