Stuart asked me a question about the 13th Age Rogue class yesterday and to answer I dug out my copy of the rulebook; I also found my GM notes for the campaign I ran back in 2014. The campaign went on hiatus as my group moved on to other things but it did not finish; what surprised me most as I looked over my notes again was how much was going on!
13th Age characters also have relationships with the Icons of the setting; these are the sort of powerful NPCs that every fantasy setting has, like the Archmage, the Orc Lord, and so on. Player-characters can have positive, ambiguous, or negative relationships with certain Icons, and there are various ways the relationship can play out in terms of mechanics; there's more detail on Icon relationships here.
I tended to use the relationships as background plot devices. The Three, a trio of powerful dragons, were interested in and a little scared of Sartheen, because there weren't supposed to be red dragonspawn. The Diabolist was watching and sort of protecting Amras, in case something happened and the Devil got out. Ne-0n was a servant of the Great Gold Wyrm, except the robot had suspicions it was being manipulated and, for the greater good or not, this clashed with the mechanoid's desire for self-determination.
(This led to a wonderful statement of intent for the second half of the campaign, as Ne-0n emerged from a period of meditation with an intention to free the player-characters -- and perhaps the world as a whole -- from the influence of the Icons. This kicked things into a higher gear and I was excited by the prospect of the players seizing control of the campaign narrative, but then we stopped playing.)
There's no alignment in 13th Age; rather the Icons have relationships with each other, and the player-characters' relationships with the Icons in turn suggest where they stand in terms of the larger philosophical and physical conflicts in the world. The Three and the Elf Queen were engaged in a cold war of sorts, so the elves were interested in the fact that the dragons were interested in Sartheen; as such they asked Amras to spy on his ally. The Great Gold Wyrm and his servants -- even disgruntled servants like Ne-0n -- stand against demonic incursions, but the robot was unaware of what was inside Amras. The players were under no obligation to go along with their Icons' plans, but all this going on in the background made for interesting dynamics.
That's just a brief summary. There were a couple of other characters, each with their own Unique Things and Icon relationships, and Sartheen, Amras, and Ne-0n had other relationships I haven't discussed. Even so, you can see how a tiny handful of numbers and words on a character sheet generated a complex web of histories and politics, none of which was planned when I started running the game. It's very old-school in a way.
Even if I never play 13th Age again -- and I do hope that is not the case -- I will have a serious think about pinching the One Unique Thing and Icon mechanics for the next game I run, because they generate so much potential fun.