to make things as not confusing as possible, my rule of thumb is:
yyyy-mm-dd (yyyy instead of yy ensures that it's not mistaken for dd-mm-yy) (hyphens can be replaced with underscores)
dd.mm.yyyy (yyyy same as above) (really dislike using for filenames, sorting doesn't work)
mm/dd/yyyy (only if there is no other choice)
edit: mm/dd/yyyy vs mm/dd/yy doesn't matter because both make 0 sense already
edit2: i forgor to say that yyyy also avoids y2.1k and subsequent issues
Going day to day, dd/mm/yyyy works, but for archival purposes and looking up stuff in the past, mm/dd/yyyy works better, imo. Like when you need to go through a physical file cabinet, or an electronic database.
Or you're the type of person who's zoned out all the time and don't even know what month it is until you look at a clock or calendar.