Open your eyes...
Three decent expansions that almost never get played at my house. They're all pretty interesting, though. BC&B in particular changes the game in a major way, as the bridges allow fields to continue that would otherwise be cut off by roads. Seems like most every time I've played with this expansion the winner was whoever managed to score the super-farm that is inevitably created by the end of the game. It actually might be an interesting experiment to play this expansion without using farmers. I don't like the bazaar component though, and always leave it out.
I&C is a classic, but I don't personally use it much because I feel like too many expansions make the games take a little too long, and I'd rather play Traders & Builders or Hills & Sheep. Definitely worth owning though.
And I like Abbey and Mayor ok but consider it far from essential.
I personally don't really care for Bridges, Castles, and Bazaars. The bridges just feel like a clunky mechanic that allow the players to "cheat" the very core rules of the game (placing tiles and matching up their edges). Plus, they take up way too much space in the box.
The bazaars are also clunky, and really don't work well at all with 2 players.
And the castles are worst of all. They're confusing to score and they add one more thing that you need to keep track of and try to remember every time a feature gets completed. I'd be genuinely surprised to ever see a game where the castles are played 100% error free.
Abbey and Mayor, on the other hand, I like. I agree that it's not "essential", but it adds some neat and easy-to-understand mechanics to the game.