I'll try to list what I remember from old discussions (keep in mind much of this might not be current):
Age of Mythology
Greeks - Originally (still?) used AoM Greek voicesets. Ruins are inspired by AoM architecture.
Romanians - The Raven is probably somewhat inspired by Odin, and the Corpsepult may be a Pestilence reference? Not entirely sure on this one.
Egyptians - Originally (still?) used AoM Egyptian voicesets. Ali Pasha's empower is based off of the AoM Pharaoh's same power.
Danish - Their design has changed some, but it's no secret that their original design
influenced by - or a direct reference to - AoM's Norse.
Tupi - Too lazy to go through all of the powers here but they are generally all built off of AoM God Powers.
Inca - See above.
Mapuche - See above.
Maltese - It's minor, but their Quick Defenses power is based off of Hades's Sentinels.
Africans - Unit weapon/shield upgrades (is this just Zulu? Ethiopians?) are based on AoM Greeks' weapon upgrades.
Also Incendios should be mentioned as being originally inspired from the Forest Fire power.
Age of Empires II
Maltese - Their unique roster's roles are based off of AoE2's unit roster, including:
- Maltese | AoE2
- Warhammer | Militia
- Ranseur | Spearman
- Footman | Eagle Scout
- Longbowman | Archer/Longbowman
- Cranequier | Skirmisher
- Hoop Thrower | Hand Cannoneer
- Knight | Knight
- Longswordsman | (I believe this is unique)
- Battering Ram | Battering Ram
- Demolisher | Petard
- Trebuchet | Trebuchet
Sioux - ¯\_(ツ)_/¯
Aztecs - Is this just because of the Jaguar Knight? Because many civs share a UU with their AoE2 counterpart. Plus with the Nahuatl Rework I'm not sure the Jaguar Knight will be sticking with us.
Ethiopians - ¯\_(ツ)_/¯
(I've never played any of the games below, so there will be some gaps)
Zulu - Youths are inspired by Zerg Larvae (originally Ethiopians had an ability based on Zerg Creep, but that went to Zulus in the way that their buildings allow certain Youth maturings)
Chileans - ¯\_(ツ)_/¯
Swedes - Night Elves do not destroy trees when gathering from them, which I believe used to be an idea for Swedes. There may be other tree-related powers.
Canadians - Probably more tree stuff.
Romanians - ¯\_(ツ)_/¯
Literally every civilization's theme
Italians - ¯\_(ツ)_/¯
Germans - ¯\_(ツ)_/¯
Habsburgs - Age-up is based off of Austria's Diplomatic Marriage ability.
Paraguayans - ¯\_(ツ)_/¯
Mexicans - ¯\_(ツ)_/¯
Rise of Nations
Africans - Age-up system of aging automatically when Library techs are researched is based on RoN's very similar system of advancing in Age.
Koreans - ¯\_(ツ)_/¯
Americans - ¯\_(ツ)_/¯
Australians - Ramping cost concept is based on RoN's similar system for units.
Colombians - Food trickle is based on RoN's Lakota.
Inca - Coin trickle is inspired by RoN Inca, which generate Wealth and Metal while mining.
Feel free to help fill in the blanks!