I am curious with current technology and tools, are we capable to sniff up and down stream of any open/closed wifi router without connected into it?
At first - strictly speaking - your wifi router is most likely two things. First: A wifi switch and second a router (and probably a lot more). The thing you want to attack is mist likely the wifi part as you state you dont want to initiate a connection.
Since wifi is no strictly directed method of message sending, packets will be broadcasted and that's it. So: If the wifi is unencrypted you can simply use a wifi-card and put it in "monitor mode". That means it will simply accept all packets flying though the air. Since everything in an open WiFi is plaintext you can read the contents (until transport encryption kicks in). If the Wifi is encrypted you can do the same as well but you will only get encrypted content. Under certain circumstances decryption after capturing is possible (see Wireshark-Wiki). You will need at least need to know the AP's SSID and PSK for that.