MySQL
http://www.mysql.com - the official MySQL database server website

PostgreSQL
http://www.us.postgresql.org - the official PostgreSQL database server website

PHP
http://www.php.net - the official PHP website
http://php.resourceindex.com/Documentation/ - guides on php; including how to install it, an FAQ, and list of php books and tutorials.

Scripts
http://www.hotscripts.com - a huge collection of links to free and commercial scripts
http://sourceforge.net - the biggest open-source host for all kinds of scripts
http://www.dhtmlshock.com - free javascript and dhtml code.
http://www.dynamicdrive.com - free dhtml scripts.
http://php.resourceindex.com/Complete_Scripts/ - free php scripts.

Script tutorials
http://www.devshed.com - well-written articles on php, mysql and other server-related topics
http://www.webmonkey.com - great articles on php and mysql
http://www.zend.com/zend/tut/ - long and well written php tutorials for both advanced and basic users.
http://www.newbienetwork.net/sections.php - tutorials on various aspects of MySQL and php.
http://www.webmasterbase.com/subcats/53 - tutorials on php and MySQL.
http://www.thefreecountry.com - has not only php/mysql related things but nearly every language commonly used and some not so common (such as fortran and cobol), they have a php/apache/zend install tut as well as code examples and tutorials.
http://www.phpbuilder.com/columns/ - Excellent tutorials on PHP programming. Aimed at the advanced or intermediate programmer.
http://www.php.net/manual/en/ - Offical PHP docs

Free hosting
http://www.spaceports.com - offers free webhosting including php and mysql
http://www.tripod.lycos.co.uk - offers free webhosting including php and mysql
http://www.multimania.com - french host, offers php and mysql

Recommended paid hosts
http://www.myacen.com - Prices are very reasonable and support is great.
http://www.solidinternet.com - A branch of MyAcen designed mainly for personal use also with very reasonable prices.
http://www.jdn-internetdiensten.nl - for dutch people. good service and not too expensive
http://www.intrahost.com - US company offering good and not too expensive webhosting
http://www.hosttoday.co.uk - UK hosting company that offers cheap hosting
http://www.hosteurope.de - German host
http://www.puretec.de - German host
http://www.featureprice.com - US host, servers are fast and worth the price
http://www.phpwebhosting.com - US host, OC12 connection, fast, friendly tech support
http://www.hostway.com - US host, not cheap but fast and phpBB works well on thier servers
http://www.alwayswebhosting.com - american, feature-packed host
http://www.interland.com - US host, not cheap
http://www.phpbbhacks.com/hosting - the hosting plans by phpbbhacks.com
http://www.darkblizzard.com
http://www.doreo.com - run by a person I know