I'm a WordPress developer (plugin and theme author, WordCamp speaker, etc), so I'm somewhat biased, but WordPress gives you need to build a user/profile site like about.me.

Out of the box, WordPress ships with an easily customizable user API with different role and capability levels. By default, meta information like name, email, short bio, etc are associated with each user. With some pretty simple development, you can add custom meta information of your own. Once you have your user configuration set up, it's pretty simple to output these users and their associated info in any number of ways, including as an all-inclusive directory and as single-user profile pages.

There are certainly other details you'll want to consider, and it would be good to know more about any specific design and/or functional specs you have, but I'd say WordPress would be an easy fit for this one.

Happy to answer any other questions you might have.