Here is what I do with my great people:
Great Spy:
The plan of attack is that I designate a city to be my super-spy city. Preferably this will be the capital, due to the +4 spy bonus from the Palace. The first Great Spy (unless it's really late) will just settle in the city, since it would give a greater yield than building the Scotland Yard yet. Next one builds the Scotland Yard, and all subsequent settle in the city, unless it's getting close to end of the game, in which case it is mathematically advantageous to do a spy mission.
Great Engineer:
Ancient Era: Not gonna happen
Classical Era: Rush a wonder, preferrably Pyramids (espcially if I pre-planned it like that)
Medieval Era: Rush a wonder, preferrably Apostolic Palace (BTS) / save and aim for Taj Mahal (non-BTS)
Renaissance Era: Rush a wonder, preferrably Taj Mahal
Industrial Era: Rush a wonder or plan to rush a wonder
Modern Era: Wait and rush the space elevator (my games usually don't last this long or head for this victory)
Of course, all the rushing depends on which strategic resources I have.
Great Artist (if not specifically going for a cultural victory, in which case mass settling and such occurs):
Depends on the game plan (read above). Usually there isn't a city that could benefit much from an artist, and it's more useful to just bulb the artist. Building the corporation Civilized Jewellers isn't all that useful either, but I'd do it for the money and spread it abroad.
Great Merchant:
I calculate how much money I'll receive from the merchant settling vs. mission and take a decision. Obviously, late game the latter is more advantageous, but I might decide to build a corporation instead, depends.
Great Scientist:
This is all a matter of calculation. Settling almost never is more useful, although there are rare times and rare windows of opportunity. Early game, I academies are extremely useful, after making sure with a calculation (even not accounting for increasing science output they're still more useful). Late game, it's more logical to bulb them, but with the advent of corporations, that could be an option.
Great Priest:
Depends heavily on the game type. If I'm playing a just-for-fun game, I'll try to get as many religions and bulb them before building shrines. If I'm playing a serious game, I'll have to think about it a bit.
Ancient Era: Most likely build a shrine
Classical Era: Most likely build a shrine
Medieval Era: Build a shrine if the good religions' shrines haven't been built... otherwise settle
Renaissance Era: Most likely settle
Industrial Era: Most likely settle
Modern Era: Likely settle, although I might bulb seeing as it's late in the game
Great General:
I designate my unit-producing city. In that city, I'll build Heroic Epic and West Point. The first two great generals settle in that city. The third great general will settle in the next best unit-production city. The fourth will settle in the next, and so on.
Usually I'm involved in enough warmongering that I end up with a unit of the required experience, especially since I start to notice which one of them are getting good and start protecting them. If truly necessary and unlikely that I'll get it by conventional means, I'll attach a warlord to a unit to get the necessary experience.
This plan works out that my HE+WP creates level 3 units, and other production cities create level 2 units.
I will only ever consider building Military Academy if I'm going for a cultural victory.
