I mostly play against AIs on Deity so most of the early game wonders are a bust, and if I want the bonus, I usually end up just taking the city that has it. There are, however, some wonders worth mentioning:

• Petra: In very rare situations, the AI will not build this, giving you a free overpowered wonder if you notice none of the civs got it early on. However from my experience, AIs will build this even if they are literally on a 1-tile desert; on maps where you start in a location that really benefits from it, it's likely several other AIs will spawn in deserts as well, so it's really improbable that Petra won't be completed by another civ. I'd only suggest risking Petra if you are the kind of person who likes savescumming. (You will pretty much never get any other useful Ancient or Classical wonder)
• Eiffel Tower: If I'm ahead in tech and can spare the faith for a GE to rush it, I will; free happiness is always nice. Sometimes another civ does finish it, but like Notre Dame, it's not much of a problem to just conquer the city that has it, as the happiness from the wonder will pay for the annexation penalty.
• Leaning Tower of Pisa: I only get this wonder if I have a Great Engineer and can rush it in one turn, since the bonus makes this wonder essentially free future GS generation.
• Porcelain Tower: Great bonus, and AIs don't get Rationalism to unlock the ability to build it.
• Hubble Space Telescope: 2 free GS? Sign me up! Use your faith to buy a GE to rush it as soon as you unlock Satellites. Even if you are not going for a Science Win or worried about an AI getting it, the two Great Scientists are too good to pass up.