All Replicant-supported devices need non-free firmware to be loaded to make the internal WiFi work. See the WiFi research page for more information. Free replacements for the non-free firmware do not yet exist.
free firmware for adapters with AR9271 chipset
OTG-cable needed
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)
Known issues for USB networking apply here, too.