A convenient way to store online and share selected photos and videos would be good. I don't trust FB/Google with images of myself and my family or my geo-tags. I would automatically be similarly sceptical of Yahoo bet a quick glance at the main TOS didn't show anything obviously objectionable.
Other than that, Flickr is one of the most privacy-conscientious services I know—which is why it took me by surprise that there weren’t controls for my favourites.
Flickr’s (general) emphasis on privacy and ownership rights are their main features to me. Maybe those are just hold-overs from the early days when monetizing your users’ data weren’t in vogue, though.
I've also asked a question on that topic.
I can have public photos, photos of family events and pictures from drunken escapades on the same account and I can reliably and easily have just certain people have access to them via guest passes.