As others have said, named suites like King Kamehameha, Grand Suite, Disney Suite, Newport Presidential Suite, etc. Especially at popular travel times like Spring Break, Thanksgiving, Christmas, New Years.
Room types with 1 or limited numbers like certain deluxe rooms or Treehouse Villas, CC Cabins, Bungalows, etc.
Of course your experience may vary. I've seen most of these fairly last minute at times too.