Great Priests are usually a good GP to settle, the hammers are nice and so is the gold. But when you will need a golden age, i'd save the Priest for that ofc. But usually, when you get that Priests really early in the game, it's not too bad to settle him directly, for example if you know you'll need that Golden Age in ~80 turns... you should be able to generate another GP for that by then.
Yes, a early priest you get from say, oracle, stonehedge or such is abit painfull to figure out what you should do with.
The early gold and the two extra hammers are nice, but a early golden age to swap into HeraldRule/caste or such smoothly can take priority. I completly agree.
Great Engineers... well, i find myself to often settle GEs as they usually occur late in the game. That's the point where rushbuilding is weak, and so is bulbing. Earlier on, i'd use a GE in 99% of the time for rushbuilding, while the other 1% is to bulb machinery when i x-bow rush with Sitting Bull

The other GREAT use for GEs are corporations, ofc. Mining Inc. is sick.
I have not played around much with corprations, I find most games won (or lost, or simply too boring) by that time.
They are not much of a issue, however. You seldom get a great engineer early.
Great Artists are weak settled and for their "special ability", the culture bomb. Best used for golden ages. Ofc, when you're aiming for a cultural win, it's the bomb, but you won't see me going cultural often.
I have settled the great artist from music a couple of times in new cities that just needs a border pop, the extra beaker bonus the settle great artist gives (or is it gold?) is a small small bonus, that still make it favorable compared to the culturebomb in this situation though.
Great Scientists have the best bulbs and are tied for the best special ability with Great Engineers in my eyes, so it's one of those two. But when you're running Representation, settling them will give you 30 BPT in oxford + observatory, so that's sweet as those are hard beakers you'll always get no matter how low your slider is.
Yeah, the bulbs form these fellows can't be ignored, especially bulbing machinery/engineering or simply philosophy. Awesome trade value or rush value.
I do tend to build academies in some secondary commerce city at times too, when the beaker value is equal or close to equal. In the end, the cottages will have matured enough so that the academy is the favorable choice.
Great Spies are great for Espionage Missions... this can easily net you 2-3 major midgame techs for free. Settled they're rather weak, their special building is great for an espionage economy which i rarely use myself. I'd rather not settle them and use them for a GA.
Same, SY in espionage economy, or espionage mission if I am unlucky to get them in a regular game.
Don't think you can run a GA with these fellows, right?
Great Merchants are the second worst GP to settle, their great strength are trade missions. Let's you fly through the midgame techs. Also, they're great for the best corporation in the game, Sid's Sushi, so it's worth holding on.
Now, I want to make a argument for settling great merchants.
If you have:
* Slider at say 80%.
* A commerce city with oxford, academy, library and univ.
* A city with with market, grocer, bank and wallstreet.
Settling the great merchant in your moneytown, will multiply the gold he generates (6) by 3!
Netting you 18 gold points per turn.
Those 18 gold points per turn doesn't have to be covered by your cottage city anymore now. So the cottage city have 18 additional commerce points that can be allocated toward research.
Since the commerce city has oxford, academy, etc. Those 18 commerce will be transformed into 54 beakers per turn.
Now, this is a extreme example, and the accual return will be abit less if there is allready market/grocer etc in your commerce cities. And other factors might also play a role.
But I hope that I have at least somewhat shown the potential strength of a settled merchant.