I manage a lot of websites under Wordpress and Let me produce a kind of user interface which I'd have the ability to see a listing of sites and also the Wordpress version they're running on.

How does one do this?

I ought to point out that those sites are located on different servers.

You need to produce a db with all of databases plus they passwords and servers (for connecting towards the other servers) and retrieve the version, or produce a wordpress plugin to wordpress that prints the version only when you signal some password from get or publish (for security reasons), and do the installation into all wordpress systems, then you definitely just browse the wordpress plugin url. (this really is helpfull without having direct accessibility mysql, this occurs on some hosting companys which have the mysql db on the closed network. )

Personally, i'd choose to choose my secound option (bolded)

EDIT: Please within the wordpress plugin use Hash protection, or something like that like this:

Your Platform Side:

$version = file_get_contents("http://www.example.com/yourpluginurl?pass=".md5($mypass+date("d"))); 
if(isset($version) && $version !== false){
    //your code here

Wordpress plugin Side:

if(md5($mypass.date("d")) == $_GET['pass']){
    //Get version here

For every site, browse the generator meta tag.

You might FTP in and obtain the version from wordpress-includes/version.php. But CuSS' suggestion of the wordpress plugin is the easiest method to go, IMO.

A lot more secure to make use of Curl or TFTP to question the file version.php at serverroot/wordpress-includes/version.php You don't need to call the database or use a wordpress plugin. You may need a local database of logins/passwords.