I decided to download the assigned port numbers from IANA, filter out the used ports, and sort each "Unassigned" range in order of most ports available, descending. This did not work, since the csv file has ranges marked as "Unassigned" that overlap other port number reservations. I manually expanded the ranges of assigned port numbers, leaving me with a list of all assigned port numbers. I then sorted that list and generated my own list of unassigned ranges.
Since this stackoverflow.com page ranked very high in my search about the topic, I figured I'd post the largest ranges here for anyone else who is interested. These are for both TCP and UDP where the number of ports in the range is at least 500.
Total Start End
829 29170 29998
815 38866 39680
710 41798 42507
681 43442 44122
661 46337 46997
643 35358 36000
609 36866 37474
596 38204 38799
592 33657 34248
571 30261 30831
563 41231 41793
542 21011 21552
528 28590 29117
521 14415 14935
510 26490 26999
Source (via the CSV download button):
http://www.iana.org/assignments/service-names-port-numbers/service-names-port-numbers.xhtml