It really, really depends on whether you're playing multiplayer or singleplayer. It also depends on starting location.
For example, Kasbah vs. Polders: Morocco have a Desert start bias, while Netherlands have a Grassland bias. Even if Polders are better on Floodplains than Kasbah, the chances of Netherlands starting in a location where they can reap the most benefits out of Polders is much lower than the chances of Morocco starting in a location where they can get the most out of the Kasbah. In addition, Polders can only be built in Floodplains and Marshes; the former is found in Desert (while Dutch spawns in Grasslands), while the latter forces the Dutch to keep Marsh tiles (which are bad) for the first third of the game before they get Polders, and that part of the game is when Marsh's -1 Food hurts the most.
Petra is nice, but don't forget that it's a) a world wonder (so you're not always guaranteed to get it, and if you do, it's only ever in one city) and b) it needs to be built in a city with terrible land (non-Floodplains Desert is terrible without Petra, though Desert Hills and Oases are OK), so you'll be stuck with a terrible city if you miss Petra and you'll often need to rushbuild it with a GE because your Desert city just isn't going to have enough hammers to finish it on its own. This is also where singleplayer vs. multiplayer comes in: the AI has a fairly low priority of building Petra, so if you rush it in singleplayer, chances are that you'll get it, while things will definitely be a lot harder in multiplayer, where most human players know the value of Petra.
I'm definitely going to agree with joncnunn on this one, the Inca Terrace Farm is amazing: it not only lets you build what are essentially farms on any hill tile (not just ones next to rivers), letting you get both hammers and growth out of them, but it's also buffed by nearby peaks to the point where what was an almost useless tile before (peaks are only really useful for Observatories and the wonders they unlock) to a tile that can potentially net the city as much food as Lake Victoria (6 terrace farms built around a peak = +6 food in total from that one peak). They're also unlocked at Construction to boot, which is a high priority tech anyway for Colloseums and CompBows. Remember that Construction is also an early classical tech, while Kasbah's Chivalry and Polder's Guilds tech requirements are both medieval.
As for the other unique improvements, they're either bad due to opportunity cost or just flatout bad. Chateau's usefulness is suspect (+1 gold is nothing, +2 culture is OK but not brilliant compared to the food or hammers you'd get out of a mine or a farm, +50% defense bonus is extremely situational), and the fact that it can only be built at Chivalry (when your culture game has advanced enough that +2 culture isn't as important anymore compared to +2 food from farms) and only on tiles next to luxury resources seals its fate. The extra yields after Flight are negligible, as Flight comes late enough in the game that the lost food/hammers from not having another improvement on that tile for the first 80% of a game is not made up for by the extra culture yield in the remaining 20%. Moai's are even worse than Chateaus on most maps: even if you can build enough of them next to each other to make their culture yield worth the missing food/hammers from not building farms/mines, the cities that can work those tiles will often have such low population due from lacking food that you won't be able to work all your Moai tiles anyway. The Maori bonus from Moai's are essentially useless (since warriors get phased out so quickly), and the bonus yield after Flight is not enough for the same reasons as the Chateau's yield bonuses after Flight.
Brazilwood camps are fine on paper, but they do have three major shortcomings that are more apparent in multiplayer than in singleplayer: jungle tiles, the need for Acoustics to get culture yield, and Free Thought. The problem with Jungle tiles is that their are a hindrance in the earlygame: if you settle a city in place where you intend to build a lot of Brazilwood camps, they'll generate a lot fewer food and hammers than if you settled a non-jungle city (exception being if you're really lucky with Bananas and Citrus). The problem with Acoustics is that it does not lie along the best tech paths to quick ideologies and factories, so you'll often find yourself picking it up after Banking, the tech that brings the gold yield from Trading Posts up to par with the gold yield from Brazilwood camps. Finally, the problem with Free Thought is that it's a Rationalism policy (so you'll always be picking it up) that grants Trading Posts +1 science, which makes the yield difference between Trading Posts and Brazilwood camps quite small (+2 culture is only slightly better than +1 science). These three combined don't make Brazilwood camps bad per say, they just don't make them so much better than Trading Posts; plus, Trading Posts unlock at a bit earlier at Guilds than Brazilwood camps' Machinery. The bonus from Terrace Farms is just so much better.