It can be done. Everything has a web interface on it these days. Cameras, printers, even our security system.
I would imagine you would allow the website to call scripts on your the machine that interacted with hardware. You would have to set the permissions correctly in your browser, however.
You seem to be mixing up the roles of client and server. Your camera has a web interface that can access the local hardware because it has a web SERVER running on the camera, the web server can be configured to access whatever resources the admin has allowed it to. In this case your computer is the client and is accessing resources on the server.
The OP was basically asking if the reverse is possible, ie is it possible for a web server to access resources on a client. The short answer as others have stated is no, there are just too many trust issues involved. The long answer is that it depends on what the OP means by "access". For instance it's certainly possible for a user to upload files from the hard drive to the server, but the web server can only see what the user has allowed it to see. It cannot for instance list a bunch of files and then select the file it wants without user interaction.