To run WordPress your host just needs a couple of things:
PHP version 5.2.4 or greater
MySQL version 5.0 or greater
The requirements have changed as of WordPress 3.2. The minimum requirements for WordPress 3.1 are PHP 4.3 and MySQL 4.1.2.
Drupal 7 will only support MySQL 5.0.15 or higher, and requires the PDO database extension for PHP
Recommended: PHP 5.2 for Drupal 5 and 6, PHP 5.3 for Drupal 7
Required: PHP version 4.4.0 or higher for Drupal 5 and Drupal 6, PHP 5.2.5 or higher for Drupal 7
and backup: viewtopic.php?f=18&t=190
Ideally, what ever happens you should be able to recreate your site in two hours or less. If you don't want your site to be down for maintenance (you can miss some inbound links if your site is (frequently) down for maintenance) we recommend that you upgrade your site via ftp if that is an option. We have also experienced that a WordPress upgrade hang, and even with fairly long IT experience, it took us about an hour to fix the problem.
So what does the above requirements mean? I means that if you use a hoster that is slow to upgrade php / MySQL, you may not be able to upgrade your blog or content management system. If you are in doubt if your host has the necessary requirements ask and ask on forums about the last requirements. It may sometimes pay to follow the front. As explained on this bulletin board, we waited years before we upgraded our other forum http://www.forumnorway.com/ to the latest version. We decided to upgrade when there were too many bugs and security holes in the old platform. And we did that upgrade in steps like this:
[*] Upgraded to the latest version of phpBB 2.*
[*] Upgraded to the first version of phpBb 3.
[*] Upgraded to the last stable version of phpBb 3.*
That may be the most secure way to do it even if it could be possible to upgrade directly from our version of phpBB 2.* to the last stable version of phpBb 3.*. So unless a lot of bugs and security holes are fixed and you don't necessarily need the last features, it may pay to wait until you upgrade. Content is King, and time is money. Especially, when a new version from Drupal 7.* to Drupal 8.* and from Wordpress 2.* to WordPress 3.* is launched, it may pay to wait some months before you refactor or upgrade your platform.