which browsers do not send referer information?
All the popular web browsers send referrer headers, at least by default. Some web browsers give their users the option to turn them off. (Example)
Referrer information not sent with a Flash http request
http://training.sessions.edu/resources/SoftwareDesignTips/current/flash.asp
For example, if someone clicks on flash banner linked to your site, request can come to your server without HTTP referrer information
This is not dependent on the browser make/version, but on the browser configuration. All decent browsers with default settings will send it, but the enduser can configure it to not send it. It's also dependent on the environmental software. If you have for example Norton AntiVirus/InternetSecurity installed, then you can configure it to let it block or spoof the referrer header with something entirely different, regardless of the browser used.