Are WiFi transmissions over an open network encrypted?

Question

By "open" I mean the router does not require a password to connect.

Answer 1

No. There is no encryption (to the router) unless WEP or WPA is in place.

Answer 2

It really depends. If you are browsing a website that is using SSL/TLS like Facebook or Gmail (if enabled) then your communication stream is still encrypted. However, there is no facility to encrypt traffic between your machine and the WiFi router unless WEP or WPA are enabled. Additionally even with WEP or WPA turned on, once the traffic leaves the router and enters the wider Internet - unless the stream itself is encrypted - WEP and WPA no longer protect that data.