One of the most annoying limitations of both Windows XP Home and Vista Home Premium was they did not remember network passwords after reboot. Vista even had a 'remember password' check box which did nothing.
Does Windows 7 Home Premium remember network passwords?
Edited to add: I am talking here about network shared resources, like \\server\music or something, not wireless access passwords.
Also Edited to add: I have now tried this on the final release, and passwords can be remembered, although sometimes this requires manually setting of username/password in the 'Credential Manager' in User Settings in Control Panel.