In an old message on this forum titled "Vista asking for a password on XP" (http://xxx.computing.net/windowsvista/wwwboard/forum/15.html), the author wrote that "Vista see my shared folder on XP, i manage to be able to see Vista shared folder(s) on XP, but when i click on the folder/link it ask for a user name and password....thing is that i don't have any password on any comps what so ever."
My Vista computer could also recognize and share the public folders on my XP machine, but my XP machine could not access the Vista Public folders because I was asked for a Username & Password, and nothing would work.
Just as in this later message to another forum (http://www.compatdb.org/ubbthreads.php/ubb/showflat/Number/177609/page/1), I verified that 'Network discovery', 'File sharing' and 'Public folder sharing' were set to 'On' (in addition to ensuring that users accessing Vista's Public folders had full permissions, and that 'Password protected sharing' was switched off.
I continued to have my XP machine ask for a Username and Password. It was only after I went into "User Accounts and Family Safety | User Accounts" in Vista and added a password (I had wanted it to be left blank) that I was able to access the Vista Public folders.
For normal connection problems, see "Vista - XP networking" at http://winhlp.com/node/179