I recently found CSS3 PIE and it's working great on my hosted site. However, it doesn't work on my localhost. In example, I see rounded corners on my webhost in all IE versions, however, I don't see it on my localhost, althrough all the code is same, behavior URL is OK, etc.

When I try to open PIE.htc file directly in browser (on my webhost), I see file's content. However, when I try to open it directly in browser (on my localhost), it shows a blank page.

Any ideas?

This sounds like it might be a known issue (see Serving the correct content type).