Let's discuss how to use Great People to their greatest effect. First, the tech discovery seems pretty pointless, with the exceptions noted below. A tech discovery that you don't even choose just doesn't seem that useful given the opportunity cost. I have only used GP's to create a golden age once, but I think that might be the best use of them actually. It is really hard to argue with a golden age, especially if your Civ is more than say 5 cities or so.
Artists
The culture bomb can be effective if you're in a severe culture war. Otherwise, I think these are almost always best used to produce a golden age. The turn based culture+research does not seem worth it - if you need culture use the bomb (+4000 now is better than +4000 over 300 turns)
Engineers
I really like these ones. Hurrying a wonder can really be useful, as can the large production bonus. I tend to use the latter, unless there's a wonder I really need.
Merchants
Never had one of these. The trade mission seems awfully risky, though. Golden age these puppies too?
Prophets
Never had one.
Scientists
The Academy seems pretty good...
Artists
The culture bomb can be effective if you're in a severe culture war. Otherwise, I think these are almost always best used to produce a golden age. The turn based culture+research does not seem worth it - if you need culture use the bomb (+4000 now is better than +4000 over 300 turns)
Engineers
I really like these ones. Hurrying a wonder can really be useful, as can the large production bonus. I tend to use the latter, unless there's a wonder I really need.
Merchants
Never had one of these. The trade mission seems awfully risky, though. Golden age these puppies too?
Prophets
Never had one.
Scientists
The Academy seems pretty good...