If you're using Debian 7 (Debian Wheezy), you need to install PHP itself and a small number of extensions. Most of what was mentioned by @Rarst is already included with one of Debian's most basic PHP installs.
You have four options in Debian Wheezy: libapache2-mod-php5, libapache2-mod-php5filter, php5-cgi, or php5-fpm. I choose php5-fpm but it all depends on how you want your web server and PHP to interact.
You also need PHP to use MySQL. Your options are php5-mysql and php5-mysqlnd. php5-mysqlnd is native and generally faster. Some might choose an alternative like MariaDB.
Graphics Library Optional
If you want your images resized, you may install either php5-gd or php5-imagick. php5-imagick will give you better quality and Wordpress will use it if it's available. If both are installed, php5-imagick will be used. If neither is installed, images will not be resized (and Wordpress won't complain).
If you install php5-curl, it will be used but is not required for anything except perhaps better performance.
Nothing else is required by Wordpress and most extensions, though some extensions may have other requirements.
Here is the complete basic install line to give Wordpress everything it needs for optimal performance and nothing it doesn't:
apt-get install php5-fpm php5-mysqlnd php5-imagick php5-curl