The official eLinux wiki provides information about Verified Raspberry Pi WiFi Adapters. Unfortunately not all devices have been tested for AP (Access Point) functionality, which is a core requirement for building a Pi(rate)Box. Look for the Chipset of supported devices, other devices with the same Chipset will also have AP functionality.
The following USB Wi-Fi Adapters are confirmed as working out of the box with the PirateBox:
Please note: Some USB Wi-Fi Adapters will only work with a compatible USB hub. More info about compatible USB hubs on the eLinux Wiki.
If you know of an adapter that is confirmed working and not listed above, please report it in the PirateBox forum. Please also take the time to mark the device AP capable on the eLinux wiki.
Edit /opt/piratebox/conf/hostapd.conf and put a # in front of the following lines
driver=nl80211 ieee80211n=1
hostapd needs to be exchanged for that device. See this forum thread for a detailed HowTo