Overall, I find that I tend to build a good mix of stuff. Depends largely on the city, though, and I'm restricting myself to city improvements here:
I build practically no castles. Short usage, not worth the hammers, free trade route disappears almost as soon as it appears, etc. It's all been said before.
I, on occassion, build walls. I find it helpful to draw the AI's initial attack into my lands and use my mobility to strike and retreat against them, so walls are built in my border cities to facilitate the use of this tactic. However, that's a personal thing--I'm not surprised to see a lot of people here avoiding them.
I originally didn't like the use of Coal Plants, but then I played as Japan (with the Shale Plant UB). Since then, I have found the 50% production bonus indispensable and definitely mouthwatering, especially if you can offset the health penalty (the only true drawback--they pay for themselves in terms of hammers in the long run).
I tend to build more colosseums (sp?) now that the cost has been reduced in the patch...but it still isn't high on my priority list. I tend to deal with happiness effectively until my cities become really huge, after which I tend to put a few of them in.
When I play Continents maps or Archipelagos (or any other water-major map where I plan on conquest), I'll build Drydocks. Otherwise, I don't.
EDIT: Woohoo! My first post since the holiday break!