(This is not intended to be an answer. Just some useful information. If you think this info is not useful, let me know, I'll simply delete it.)
I think talking in terms of packages would be easier for newbies, but since packages vary from system to system, it's hard to cover all of them.
As I have experience with Debian (& Debian-based distros), I'd like to share this specific information:
- php-apc (not required, but recommended)
The aforementioned packages install all the extensions/libraries/modules mentioned in the other answers; all, except Mime Magic, which is no longer required by WordPress.
Another good way to make sure your server is 100% compatible with WordPress is to check what packages the managed hosting companies come pre-installed with. As they have years of experience with customer complaints about incompatibilities, they'll know better.
In case of Hostgator, the PHP modules they pre-install include (you'll probably only need most but not all of them):
Media Temple provides a
phpinfo(); file for you to check their config. It's useful for comparison purposes too.