Hatoful Boyfriend (TV Tropes) - a visual novel (download, English patch), where a female protagonist attends high school with, and romances, one of a selection of giant talking pigeons and one partridge. Also she lives in a cave and forages for food. The freely downloadable version (for which there are a couple of mirrors on the TV Tropes page, if the original is acting up) is sadly not the most complete pigeon-dating experience available. There's a paid version (note from the author here explaining the differences) which is as yet untranslated. The experience of dating a Bleeding-heart pigeon will have to wait.