There is only a small amount of information that you can get via an HTTP connection.
IP - But as others have said, this is not fixed for many, if not most Internet users due to their ISP's dynamic allocation policies.
Useragent String - Nearly all browsers send what kind of browser they are with every request. However, this can be set by the user in many browsers today.
Collection of request fields - There are other fields sent with each request, such as supported encodings, etc. These, if used in the aggregate can help to ID a user's machine, but again are browser dependent and can be changed.
Cookies - Setting a cookie is another way to identify a machine, or more specifically a browser on a machine, but as others have said, these can be deleted, or turned off by the users, and are only applicable on a browser, not a machine.
So, the correct response is that you cannot achieve what you would live via the HTTP over IP protocols alone. However, using a combination of cookies, as well as IP, and the fields in the HTTP request, you have a good chance at guessing, sort of, what machine it is. Users tend to use only one browser, and often from one machine, so this may be fairly relieable, but this will vary depending on the audience...techies are more likely to mess with this stuff, and use more machines/browsers. Additionally, this could even be coupled with some attempt to geo-locate the IP, and use that data as well. But in any case, there is no solution that will be correct all of the time.