Food buildings more than pay for themselves (city growth and being able to work a mined hill)
You'll want all gold buildings to max out income.
Science is King in Civ V, so you want all of those as well.
In BNW, you often run out of spots for Great Artists after filling the palace and need Hermitage for others, this requires an Opera House in every city (and the Monument & Amphitheater prereqs). Museum is even further away, and also has Opera House as a prereq.
Only civs with Catherdrial follower belief get to build those, and both Sistine's Chapel & Uffizini is limited to whoever built that.)
So what is left: Shrines / Temples. If you want to found a religion, absolutely needed. If not, then while they can be delayed, it's beneficial to complete them before Industrial era starts anyway for a few faith based great people.
Barracks: Only the designated military unit city really needs this. But you might want to build HE anyway, which requires a copy everywhere. (Following completion, you can stop wasting money on maintenance by selling the extra ones.)
Armory / Military Academy are the same way: Only needed in your designated military unit city.
Walls / Castles / etc : Cities that will never see combat won't need them. This makes them a border city only.
Happiness buildings: Build as you need more happiness, and better to stay slightly ahead than fall behind. In addition, if planning an offensive war, then pre war you should develop a large surplus to absorb the hit they'll take when you conquer cities.
Hotels: Only really needed for Cultural victory.
Airport: In addition to the tourist use, they also have direct military application.
Constable / Police Station: The main benefit is only in the capital. Technically speaking, you can skip even there, but be prepared for the AI to be stealing techs left and right.
Note that you need a Police Station everywhere to be the NIA. (Extra spy which if going Diplomatic turns into an extra Diplomat)
Harbor: Needed in any city that's not on the same landmass as your capital, plus you need one somewhere on your mainland (in the capital if coastal, otherwise choose the best coastal city there). It's also highly desirable for cities running external cargo ship routes.
Workshops tend to pay for themselves in production between both the production to their own cities and adding production to the Iron Works city, which requires them.
Factories & Windmills are mostly for the more productive cities.
Normally buildings that require a local resource are very much worth building.
Also, unlike Civ IV, Civ V national wonders require a copy of X building in each and every city you have at the time.
