The minimum requirements to run WordPress had been announced many months ago. The requirements are PHP version 5.2.4 and MySQL version 5.0, and the minimum requirements for WordPress 3.1 which at that time was yet to roll out was PHP 4.3 and MySQL 4.1.2.
To date, I don’t think everyone is ready yet to drop their old PHP and MySQL versions in favour of the required higher versions.
Checking on the latest postings in WP.org support forum, there are discussions being exchanged on the topic like What’s different in 3.2 than requires MySQL 5? and [resolved] Need Help ” running PHP version 4.4.9 but WordPress 3.2.1 requires at least 5 (19 posts)”.
Without dismissing the concerns of those with issues on WordPress system requirements, our company experience is that WordPress 3.2.1 can still run on MySQL 4.1.2 as long as (a) the host meets the minimum PHP 5.2.4 requirement, and (b) the WordPress 3.2.1. is a “fresh install” meaning not upgraded from an older version like 3.1.
We also found out that if you upgrade to 3.2.1 without upgrading your MySQL to 5.0, your front-end WP would still run as before the upgrade but you cannot open your WP admin panel. It’s going to output an error message that “you cannot update to WP 3.2.1 unless you upgrade your MySQL to version 5.0″.