When I happen to visit Yahoo Answers occasionally, looking for this or that answer to a technical problem, I notice that the site tells me how many new emails I have. "Oh," I think to myself, "That's convenient. I should check those messages while I'm here." I don't use my Yahoo mail account much, because it's basically my spam trap, but sometimes it attracts something useful. Anyway, I click on the icon and it asks me for my password to log in. "But," I say to myself, "how did you know how many emails I have if I'm not logged in?" At this point, I usually leave, because the convenience factor is gone.
As with all security, it's probable a trade-off with convenience. Yahoo knows who I am based on some old cookie or something, but needs my password before letting me see my mail. Understandable, but inconvenient.
Mokalus of Borg
PS - I wasn't a fan of the updates they made to Yahoo mail some time ago.
PPS - They took away all the keyboard shortcuts I'd been using.