There are 14 National Wonders. The series will consists of the following four parts:
I. Flop 3
II. Top 3
III. Good. Basic. Not Game Breaking.
IV. Specific. Key for some scenarios.
We start with the worst three National Wonders. Worst means, that they are the ones that get build the least if at all in civ multiplayer (and most probably in single player as well). I myself have never built any of those three nor seen them been built in any game.
I. Flop 3
II. Top 3
III. Good. Basic. Not Game Breaking.
IV. Specific. Key for some scenarios.
We start with the worst three National Wonders. Worst means, that they are the ones that get build the least if at all in civ multiplayer (and most probably in single player as well). I myself have never built any of those three nor seen them been built in any game.
Mt. Rushmore
-25% War in all cities
+1 Great Artist point
+4
Cost: 500 normal, 335 quick speed (Double Production Speed w/ Stone)
Second Mt. Rushmore requires Fascism, one of the lowest priority techs I can think of. It´s nice of the developers to leave us with the option NOT to become a fascist . It neither brings any useful units nor buildings, nor is it a prerequisite for any other technologies. Police State has its uses, but not in a game where you have to research Fascism for it first (read about uses of Police State here. And I wouldn´t be prioritizing Fascism for a lousy Great General.. And don´t get me started on Paratroopers.. (unless nukes get allowed again (because the "nukebug" gets fixed) and even then ).
Last but not least this wonder gives artist points. Artist points bad. Baaad. On why that is the case, you can read more here in a text about the French Salon.
Due to its uses in certain situations in ffa diplomacy games Mt. Rushmore is the best of the worst of National wonders. Forget about it in "always war" games though.
West Point
New units receive +4 experience points
+1 Great Spy point
Cost: 800 normal, 536 quick speed (Double Production Speed w/ Stone)
Requires: Military Tradition and a unit of level 6 experience
First of all this one is expensive, especially without stone. Then you need to have gotten a great general (or an unusually long lasting unit that got to level 6, very rare..) - both requiring combat (or researching Fascism first ). So you cannot plan with West Point from the beginning even if you wanted to.
Another factor being that in order to make West Point worth it, you need to build it into a city that will be able to get out a significant amount of units afterwards. You most likely though don´t want to block one of the two National Wonder spots of your capital or Great People city for example since those will rather want to have economic related stuff like University of Oxford, National Epic, Wall Street, Globe Theatre etc.. Neither do you want to use your best production city for producing units instead of wonders - though this one is more likely than the other two.
Next West Point gives units built in its city four additional experience points. Cavalry come (with Rifling) short after Military Tradition which allows cuirassiers. This means if you´re planing on using Cavalry for an attack (which is common practice in longer games like ffa and Ironman), you´ll barely finish production of West Point (if you had a level 6 unit at this point in the first place) till then. This is significant because the Cavalry is the last unit that profits from stables and its experience bonus. The consequence being that even with West Point you probably won´t reach another promotion level for a long time. Three experience from Barracks, two from Stables, that´s five. Theocracy is a valid option here, Vassalage not so much due to having to give up Bureaucracy and later on Free Speech for it. Unless you're Charismatic (which you do not want to be in an Ironman or ffa), it´s likely that the West Point city will only temporarily build triple promotion units - if at all. That´s especially true once you go past Cavalry to Infantry, tanks etc. It should be at least 5 additional experience points to make this worth building - and even then the other arguments against it still apply.
I guess if you are Charismatic, have stone and a city with decent production that is not your wonder or GP city nor your capital, it can be an option, especially if you plan on waging war with Infantry, tanks and other late game units.
Red Cross
Free Medic I promotion for units built in this city
+1 Great Scientist point
Cost: 600 normal, 402 quick speed
Requires: Medicine and around 6 (depending on map size) hospitals
This is a pretty expensive wonder that cannot be produced faster with any resource. It requires you to build hospitals, which you only want to get really late in the game and only in few cities, most likely in less than six even if you have 12, 15 or even more cities in an ffa or Ironman. Also its effect isn´t very desirable. Not that a Medic I promotion (probably at least Medic II on at least one unit) is a bad thing, but you´ll likely get a healer anyway and even if not, this is not anything game breaking, especially looking at the required investment. I don´t see any situation in any setup where you´d build the Red Cross instead of something else, even if that was "just" units for those 402 (on quick speed).Resume
Those three wonders are the least desirable overall of all National Wonders - they have the least scenarios in which you´d want to build them instead of something else. Mount Rushmore and West Point might come up very rarely here or there, but only in long-lasting games like Ironman or ffa.
Mt. Rushmore is mainly a victim of multiplayer´s "always war" and its prerequisite technology, otherwise it probably gives a decent effect for the required investment. West Point would need to give at least five, probably rather seven additional experience and rather don´t have the prerequisite of a level-6 unit in order to see more play. Red Cross is hopeless the way it is right now. As a normal building for around 120 without any additional requirement besides its prerequisite technology it would see some play...
As for West Point, I´m curious to hear arguments for it in any setup.
Also remember those articles are reposts from a site relating most stuff to MP - not meaning that the majority of concepts are not the same for most SP aspects.