Suppose I've got a website located in the url:

http://world wide web.mysite.com/

Say this really is located by host company "A".

Now, I wish to host a subdirectory in this site at another host:

http://world wide web.mysite.com/blog/

...say I host this with host company "B". So that all the web pages under this website could be in a different data center.

Is configuration possible?

If you're able to configure a reverse proxy... then yes.

Apache mod_proxy

IIS reverse proxy <= it's a codeproject solution and might not have support. You are able to most likely find a lot more should you just look for reverse proxy.

If you work with IIS7 (Vista, Home windows 7, Server 2008) you can utilize the HTTP Redirect feature that's built-in.

Yes, possible.

Lately I discovered this exact problem, using IIS. For the solution we used ISAPI_Rewrite 3.

Use a simple directive in IIS with ISAPI_Rewrite 3 and also the RewriteProxy directive

If you work with Apache mod proxy works, (pointed out already here). Regrettably there is no same as RewriteProxy in Apache mod rewrite.

One caveat of the solution we'd ended up being to have rewrite rules to handle new url's to blogs.

You will need a sqiud server before both apaches for optimal results. All of the demands can come towards the squid instance, that will route it right apache according to request path.

Both apaches must be set up for your domain. DNS An archive must indicate the Squid instance.

Point the DNS record for that subdomain towards the ip from the other host.