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Full Credit goes to Pet Stilgoe:
But because I’ve had to look this up twice I want to make sure I have this information even it Pete takes down his blog.
I’ve modified the instuctions a little since his has some extra steps, but otherwise this is a cut and paste from the post above.
“If you have enabled anonymous access on your Sharepoint farm and you still get prompted for a login when trying to access a list, it is most likely that your list exists in a ‘Publishing Site’.
This is because by default all publishing sites have a feature called ‘ViewFormPagesLockdown’ activated. This basically provides extra security for internet facing Sharepoint sites by stopping anonymous users viewing pages like AllItems.aspx etc.
If you want anonymous users to be able to view such pages you need to disable ‘ViewFormPagesLockdown’
1 Remove all anonymous access from the site.
2 stsadm -o deactivatefeature -name ViewFormPagesLockDown -url
3 Make sure that the list inherits its permissions from its parent.
4 iisreset
5 Turn anonymous access on at the site level