Yerevan  (15+1) - Obvious number 1. This is the first one I upvoted, because I knew how strong it is for religious games. Now I realize it's even stronger than I first believed. It excels universally. Going for domination? Use crusade and super apostles - +10 combat strength is no joke. Use chaplains to heal your units, and use heathen conversion to recruit barbarians. Culture? Get them relics and monastic isolation. Religion is obvious. None of the above? Use your own debater apostles to crush any opponent attempting to win a religious victory (without going to war). This is the tip of the iceberg. No need to make the same arguments over and over. For me, it boils down to this: you can't do what Yerevan gives you any other way. You can get amenities, culture, science, gold, and other benefits provided by other city states in a number of ways. Choose your favorite. Yerevan is unique. If you want 4-5 debater apostles to form an unstoppable force of theologians, you need Yerevan. You want to insta-convert large ai cities? You need Yerevan.
Zanzibar  (8-3) - I haven't heard any persuasive arguments as to why this is top tier. In my games, I usually run a large amenity surplus without Zanzibar. Let's pretend though that these extra amenities do make a difference, and my city goes from being content to happy, or from happy to ecstatic. Wow, all of a sudden my cities are growing 10% more and earning 5% more food. Oh wait, not all cities, only a few (six cities get 2 at most, 12 get 1 at most). Hardly a game changer, especially since people are saying food and growth aren't limiting factors. Milta was taken out early, and that gives an extra 15% growth rate. I've never run negative amenities, but even if it did take a city out of negative, it would at most improve city yields by 5%. Amenities do not win games. Amenities do not provide culture, science, production, or faith. Only a couple civs receive any special benefit - Scotland and Aztecs come to mind. For the rest, I am scratching my head as to why people think this is so good. I have learned a lot in the elimination threads since joining the forums, but nothing so far has convinced me Zanzibar should be top 10 let alone top 5.
Edit: To the poster above, respectfully, I just don't get why Zanzibar is better than Cahokia. Cahokia can give every city 2 amenities (and housing, and gold), not just 1-2 to 6-12 cities. Yes, you need a builder charge, but it's a robust benefit that lasts even if you lose suzerainity.