The Item #13 is an obvious reference to the number.
King Ralph XI was originally named King Ralph XIII; however, at the suggestion of the player Lord Ingo, Jick agreed that it would be ridiculous and not even funny if it were XI instead.
The 2005 Advent Calendar produced aspirin with the message, "They can't all be winners, kid," on its thirteenth day, supposedly for the same reasons as noted above.
There are thirteen different colors of Slime Potions.
Other unlucky happenings:
At one time, the item number 666 was also avoided for superstitious reasons. Nevertheless, BoozerBear managed to hack 13 of them from the item database and keep them in his inventory, until one day, as a meatsink, Jick implemented the steaming evil as item number 666.
Uncle Crimbo's player ID is 666, a foreboding sign of his eventual fate.