With mobile devices, users are taking ever-growing numbers of photos every day. These photos are uploaded to social sites such as Facebook and flickr, often automatically. Yet, the portion of these uploaded photos being publicly shared is low, and on a constant decline. Deciding which photo to share takes considerable time and attention, and many users would rather forfeit the social interaction and engagement than sift through their piles of uploaded photos. In this paper, we introduce a novel task of recommending socially-engaging photos to their creators for public sharing. This will turn a tedious manual chore into a quick, software-assisted process. We provide extensive analysis over a large-scale dataset from the flickr photo sharing website, which reveals some of the traits of photo sharing in such sites. Additionally, we present a ranking algorithm for the task that comprises three steps: (a) grouping of near-duplicate photos; (b) ranking the photos in each group by their ``shareability''; and (c) ranking the groups by their likelihood to contain a shareable photo. A large-scale experiment allows us to evaluate our algorithm and show its benefits compared to competitive baselines and algorithmic alternatives.