Yes, you can do this. Use session_register to instantiate variables you need between pages. You can then unregister them when the user logs out.
Sessions have several modes of operation - only one of which requires cookies. Given the fact that Hotmail, New York Times and other mainstream sites require cookies, I don't think it's onerous to ask that users have cookies enabled.
However, if you don't want to use them, you can manually track a session id in your pages (e.g., by using a hidden field). This is just a little more work though.
Dave
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