Some of the relationships, associations or diplomatic interactions between various Civ leaders that I can think of:
1) Tomyris' deadly rivalry with Cyrus is already referenced to in her agenda.
2) Ashoka (India, Civ IV) was Chandragupta Maurya's grandson.
3) Gajah Mada (Indonesia, Civ V) was
Mahapatih or Prime Minister to Gitarja.
4) Tamar of Georgia has been recorded to have sent diplomatic missions to Saladin on his capture of Jerusalem for successful negotiations about return of confiscated possessions of Georgian monasteries in the city and for free access for Georgians to the holy city. She is also said to have unsuccessfully bid for obtaining the relics of the True Cross which were taken by Saladin as a booty of war.
5) As has been previously discussed on the '
Possible New NFP Civs' thread, Catherine de'Medici was mother-in-law to Philip II while he was married to her daughter Elisabeth of Valois. Interestingly, it was at the celebration of this betrothal that Catherine's husband Henry II met with an accident while jousting, which led to his death and Catherine's subsequent rise to power as the influential Queen Mother during her sons' reigns.
6) Philip II had famously adverserial relationships with two of his contemporaries who have appeared in Civ - Elizabeth II of England and William the Silent of Netherlands. The disastrous defeat of Philip's Spanish Armada by Elizabethan England is quite well known.
William the Silent initially served Philip's father Charles V and was later appointed as the governor of the Dutch possessions of the Spanish Habsburgs by Philip himself. Later however, he went on to become the main leader of the Dutch Revolt (which ultimately resulted in independence of the Netherlands.) This also led to Philip announcing a hefty bounty on William's head!
7) Despite sharing a surname, Indira Gandhi (former Indian prime minister and one of India's leaders in Civ3) does not have a familial relationship with India's perpetual leader in Civ, Mahatma Gandhi; she got the Gandhi surname after her marriage to a yet another unrelated Gandhi (Gandhi is indeed a very common surname in parts of India). However, both Indira and Mahatama Gandhi did have a close association through Indira's father Jawaharlal Nehru who was India's first Prime Minister post independence and a very close associate and mentee of Mahatma Gandhi during India's Freedom Movement. Indira Gandhi is known to have interacted very closely with Mahatma Gandhi in her younger days.