In the default installation for a website, you will need apache2 and php5. Of course, you can also use another webserver like nginx and another php engine than apache's mod-php.
PHP >= 5.6
The other extensions are optional and the framework won't crash (as in GTA 5).
If you want to connect to a mysql database:
If you want to use memcache (as session store or cache store), this extension will be necessary:
If you want to use the image functions: