Is there an app where you can rank songs or other items by picking 2 at a time to make a master list

None that I know of, but I can spot some problems with that:
Would it be supposed to play you the songs first? Copyright nightmare.
Where would it obtain the list (considering you haven't heard 1% of all songs composed) - your personal itunes mayhap, if you use that? I don't think such access permissions can be granted to an external app.
Binary comparison is somewhat inefficient if you have a ton of songs, especially if multiple comparisons are necessary to improve results, and possibly inaccurate in songs (moreso than facemash).
It wouldn't be of much value to anyone else without coupling to some recommender system.

That said, a rookie programmer with a list and comparison system in mind could set up a rudimentary version in a day (text based, that is). Something like chess rating might work. The additional features take up the most resources.