Where does Linux store Wifi passwords?

Ubuntu (and most likely many flavors of Debian) stores the information at /etc/NetworkManager/system-connections. Each of the connections has its own file entry. The files are secured with file mode 600 and owned by root.

The files in this directory are not limited to wireless connections; there are files for the wired connections, too.

There is no standard place: this depends on the wifi connection software. For instance, wicd stores them in /etc/wicd/wireless-settings.conf (which is a bad idea since the whole configuration file needs to be protected). So, I would advise you not to store the passwords with other settings that can be readable by everyone without having to become root.