aight, I'll add first(though these aren't an experienced player's opinions, so guide me on this one)
HL(Hanseatic League) - Besides the cool history about it, I also like that my economy starts to flourish everytime I finish it( more than GL does at classical). It does help me make the gold to spend on alot things around mid medieval: research, espionage and gold rush a building( yea I often does this to jumpstart a new settlement. I gold granary, jewelry, and (sometimes) theater). I think this is because of my bias, because I usually pick seafarer leaders, so maybe my mind will change.
Askle(asklepieion) - To anyone who aren't aware, this is the wonder that reduces plague build-up city and gives some health on the city it is built on. This wonder is surprisingly worth the hammers. turns out, less plague means more commerce on my main commerce city, since I can build more cottage without worrying about increased infestation. really gets better with increased difficulty level. It doesn't get obsolete for a long time too!(until Microscope, Rennaissance)
FA(Fortress Alamut) - This is probably exclusive to Political leaders, but what I like about this, is that, the units that you build in a city it is in will have free commando promotion, which lets my light horsemen to blitz raid enemy improvements, and catch workers off guard, and it lets me build city assault melee units and levies that can get to the enemy cities asap. The walls? well, let the spies and the wonder's bonus espionage take care of it beforehand(because, unfortunately, siege units like trebs and cannons can't receive commando promotion. would be awesome if they do though). the history behind it looks pretty cool too! you like assassin's creed? or assassins in general? or devouted fanatics? look it up!
I think that's all I can remember for now. I do remember somebody mentioning the Mids(pyramid) being good, so I always build it, but I can't intuitively feel the benefits of it positively affecting my game. I guess because of the engineer? I dunno what to do with it, though, tbf, of all my 4 games, I haven't progressed past early rennaissance, so maybe I'll need an engineer someday.
I think there's also the christian wonder that's really good, but alas, the AI got there first before I get to build it. there's also Islam's Haram esh-sharif that's pretty good for seafarer leaders.
Let me know what you guys think!
Edit: I did some fact checking on Askle