I have a Windows Azure web role with the <httpCompression> options set in its Web.Config configuration file.
On the local development fabric I can see that my HTTP response is properly compressed. When I deploy my web role to Windows Azure Staging, Windows Azure in the cloud no longer compresses the response.
If I had access to IIS7 I could also compress the response directly in IIS (static and/or dynamic content). But in Windows Azure I can't directly configure IIS, I can only use the <httpCompression> option.
There's a whole thread on this issue in the Windows Azure forums:
Azure Services Platform Developer Center > Azure Forums > Windows Azure > Serving compressed content > Serving compressed content
As I mentioned in the thread above, this would be a showstopper for me. It'll be hard to convince my boss we should use Windows Azure when on some content we'll have to spend roughly 5 times more on bandwidth than what we would with proper compression.