In my 13th Age campaign I am using relationship rolls in the way I used random encounter table in my This is Thracia Game.
I have a table for each player and their relationships and results for if they roll a 5 or a 6 for that Icon.
This article from the Pelgrane website also has some great ideas that can be used to make Icon Rolls into random encounters.
Here are some examples from my both my current and previous campaigns: (Players in my 13th Age game may want to read no further as there are spoilers to be had, or they might want to read them and pick a favorite do they can suggest it next time they roll that result for their Icons.)
Half Orc Half Elf Barbarian prophesied to be “The next big thing in Sorcery” (to bring balance to the... Magic was also suggested. She has no magical talent at all and instead sometimes seems to suck the magic out of things and store it acting like a strange magical battery.
Her Icon relationships reflect her status as a child of prophecy, Three Icons are interested in her but all seem a bit disappointed that she isn’t overtly Magical.
Conflicted Elf Queen 5 - Her magic batteryness goes wrong
Conflicted Elf Queen 6 - Her magic batteryness goes right
Conflicted High Druid 5 - Dire Animal needs help but is from the faction that doesn't like her
Conflicted high Druid 6 - Dire Animal comes to help
Conflicted High Druid 6 - Druid awakens her dog
Conflicted Orc Lord 5 - Orcs try to kidnap her!
Conflicted Orc Lord 6 - Orcs spies help her
Imported from my 13th Age of the Hungry Phoenix game. Ash is a Halfling Rogue, cook and con man. His One Unique Thing and Icon relationships all stem from a Con Job he pulled with the Prince of Shadows where a misplaces Love Potion left him fleeing from a smitten wife, who was also the Daughter of the Diabolist!
2 point Negative Diabolist
5 - Demon infested Kitchen! Maybe it is possesed
5 - Agents of Apocalyptica (his wife) find him.
5 - Demon infested item makes him take it with him or it will tell his wife where to find him.
5 - Diabolist sends agent with love potion, accidently gives it to another player.
5 - The demon that Gribnez summoned turns up to repay her favor, this should help Gribnez but will probably mess with Ash.
5 - Cultist pirates from The Circle (The Ship where Gribnez summoned a Demon) turn up, the captain might have been deposed in a mutiny because he let the players go and now he wants their help to get his ship back.
6 - Love note from “wife” with helpful magic item.
1 point conflicted Prince of Shadows
5 - Deneth Serassalion (The magic Item forger) causes trouble after discovering that he was not in fact being Punked when they broke into his warehouse.
6 - One of Ash’s old acquaintances has a package for him from the prince of Shadows. (A Magic item that might help against Demons or scrying)
The bastard son of the Archmage and The Diabolist, his half sister is married to Ash.
Diabolist conflicted - They really like him and want him to use demonic power, He wants nothing to do with them.
5 - Demon offers to help in a time of extreme need.
5 - Demon hunter turns up looking for him.
5 - Magic Sword with a demon in it
5 - His sister sends a message to him asking for help finding Ash
5 - Cultist pirates turn up (as per Ash’s result above)
Conflicted Diabolist 6 - Diabolist Agent disguised as an Agent of the tower gives him a demonic magic item.
6 - Archiraxyous (his Imp familiar) becomes supercharged
Conflicted relationship with the Archmage because while he is a loyal member of the Tower (The Archmage’s Secret Service) his parentage both shames the archmage and makes him the target of suspicion from his superiors.
Conflicted Archmage 5 - Superior demands a full report of any Demonic activity in the area.
5 - Deneth Serassalion - The magic Item forger who got Punked causes trouble
Conflicted Archmage 6 - Agent of the tower turns up with a magic item to protect him from Demonic influence.
2 points Positive with the Great Gold Wyrm: He thinks he is the Avatar of the Great Gold Wyrm.
5 - Paladin of the Great Gold Wyrm has been conned out of all his stuff and needs their help getting his gear back.
6 - Paladin of the Great Gold Wyrm turns up to lend him her aid in his struggle
1 point Conflicted Emperor: He once started a Rebellion against the empire
5 - Imperial official recognises him from an old wanted poster and tries to arrest him.
5 - Bounty Hunter turns up looking for him with old wanted poster
6 - Anti Imperial Rebel recognises him as a fellow free spirit and offers to help him in his cause against the man.