When switching from Chrome to Firefox I accepted FF's offer to import my Chrome cookies.
(This was stable/release versions of Chrome 24 and Firefox 18 or 19 on Win7.)
After this I found that I could no longer log into any of the SE sites. When I attempted to log in, the site would recognize me and display a message indicating that I was being automatically logg'ed in, but when the page refreshed I was still not logged in.