All the early game Wonders are situational. If it seems like a good deal to try for them, I'll go for it. If I can't build them quickly enough, I'm tying up a major city for too long when it could be building other stuff to expand my empire, with too high a risk that the AI will get them.
If I have a Great Engineer at the right time, I'll look at available Wonders and select one. It is almost always worth doing for any early game wonder, which the GE can build completely anywhere.
The modern Wonders, even middle ages, those are the key ones. Apostolistic Palace and the UN are must-try-for if you want to control their diplomatic power. Having a guaranteed shot at election is worth a lot.
Three Gorges Dam is pretty helpful on any large continent. Making sure no AI gets it is a pretty good reason to get it as well. Unfortunately, it is pretty hard to get it on normal speed before you've built coal plants everywhere of importance, so you don't need it so much for power as for a slight reduction in pollution. But it can be a great help for newly conquered power-less cities, especially if you use Mining Inc to boost production.
If I want a modern war I want the Pentagon. The extra experience is nice, and again, I want to deny my enemy.
Statue of Liberty is always worth shooting for. It pays pretty well, especially on larger maps.
If I have a dominant state religion, I'll try for Spiral Minaret and University of Sankore to take advantage of that, as well as of course getting the Apostolistic Palace. It can be hard to get both in a competitive game.
Pyramids and Great Library are an obvious great combo, but if I don't have stone or lots of forests or both then they aren't exactly must-haves. Instead, building an army to take them is better
