When I am trying to upgrade WordPress (current version 3.1) to WordPress 3.2.2, I am getting this stage error:
Fatal error: Out of memory (allocated 29360128) (tried to allocate 3155893 bytes) in /homepages/32/d108770064/htdocs/Wordpress/wp-includes/class-http.php on line 1420
How to fix this and update WordPress?
The only thing you could do is try and uninstall the old WordPress 3.1. Then, download WordPress 3.2.2 from the website and install the new version.
You'll need to post more information if you want us to help, such as server load, server specs, etc. But what @Giggsey said is mostly right; you'll want to download a fresh copy of Wordpress and see if that works. However, make sure you back up your files.
If you can access your PHP configuration, try increasing memory_limit to 32M or 64M and restart the web server.