All Replicant-supported devices need non-free firmware to be loaded to make the internal WiFi component work. See the WiFi research page for more information. Free replacements for the non-free firmwares do not yet exist.
However, free firmware does exist for WiFi adapters with the AR9271 chipset. Such adapters can be used with a device running Replicant 6.0. A USB OTG (On-The-Go) cable is needed to connect the WiFi adapter to the phone.
link to some external resources that explain how the chipset can be identified on a GNU/Linux system
link to useful online hardware databases
preferred
high battery drain, possible battery damage or shortened lifecycle for batteries
adapter is not powered when low battery charge
Displayed battery charge level may not be accurate (likely lower because of quick drain)
which devices work best? Note 2 (big battery) -> Galaxy S 3 -> Galaxy S 2 (instabilities, battery issues, see #1791)
Known issues for USB networking apply here, too.