Not the actual die as it's not nearby. Attribution: G2 Collectibles & Hobbies
It's a little unusual in its shape and size, which is cool, but this isn't the reason it's my favorite. I bought this die when I was running my AD&D homebrew game set in the world of Auracrux back in college. The way I decided to make use of it was this rule:
"If I have no idea how to go about making a ruling that must be made quickly, I will roll the d30. If I roll a 1, something bad happens."
My game was a game about epic heroics, prophecy, gods fighting, etc. Not the sort of game I'd run now, but fun. Two of the characters, Serrah (a name level Cleric and the prophesied "Daughter of Virtue") and her bodyguard, Varno (originally her friend Alfred, who died and was sent back to finish serving Serrah) had left the plane of Auracrux to request assistance from The Council of the Planes, a panel of 9 gods they had discovered by accident that existed beyond the monotheistic plane of Auracrux.
When they got to the outer planes, they discovered that Auracrux had been sealed off to prevent outsiders from influencing the outcome of the approaching war between good and evil. Refugees could leave, but no one could go in under any circumstances.
In retrospect, this seems sort of silly, but oh well, it happened. Really, the whole plot line of having a multiverse beyond Auracrux was a bad idea. I had recently purchased Manual of the Planes, and I thought I should incorporate it.
Anyway, this required the players to consult with outer planar sages to find another portal into their home plane. After some work, they found the portal and stepped through, without any of their normal auguries, etc. I had not determined where this portal should go, but I knew they had the magical capacity that most places on the plane wouldn't be more than a hiccup, so I invoked the d30 rule.
This led to their teleporting to the south pole, the domain of an insane wizard of incredible power whose dream was disrupting the war between good and evil and elevating himself to the level of a god. Now he had prisoners to use as a bargaining chip. This led to several weeks where the other players and some other PC's controlled by Serrah and Varno's characters penetrated the south pole, slayed the wizard, and rescued the priestess.
That's why I love my d30. I think there are a lot of problems with the way I was running my game at that time, and arguably, this was the "jump the shark" moment of that campaign, but it's the only die I have with its own story.