There aren't a lot of Outlook Express competitors, but Mozilla's open-source Thunderbird is one of the best of them. However, since a while there's a new player in town: Postbox. Postbox is a new email client built on Mozilla technology that intends to offer a new and refined way of working with email and its media.
Still in beta, Postbox takes desktop e-mail toward Web 2.0, with contacts to sync with Facebook, pictures to upload to Picasa and messages to tag (which you can compare with "Labels" in GMail). Once you get going, Postbox's tabs can be used to filter out messages and focus on only attachments, images, links or contacts burried in your email, as well as organize your email.
Postbox is written by a lot of (ex-) Mozilla folks, with the help of XUL, a Mozilla markup language for user interfaces. Although the application looks great on the Mac, I could tell after less than 5 seconds that Postbox wasn't a native Cocoa application.
Perhaps this is kool-aid talking, but in my opinion Apple Mail is much more functional, better designed and useful than Postbox. Although, I would have to admit it has some nice features and the UI looks great at first sight, the crowded layout, the non-native feel of the application and the general feelings of Postbox are left incomplete, but as Postbox is still in beta let's give the Postbox-team the benefit of the doubt for now and wait for the stable version to make a final judgment. After all, Postbox is currently the only Mac email client that supports features such as social network integration and tagging within an e-mail client.