I know each Great Person type gives benefits like extra science, or commerce, or culture, or hammers, but I seem to recall seeing things that indicated that they also increase the rate of GP generation, but cannot now see it or find it.

ADDIT: I've recently come to realize some of the benefits of the Great People that I previously had not appreciated.

Lets say it is getting to be about middle ages. You've done some early game expanding and fighting, and now based on your civics your economy is a bit over-stretched. Lets say you can only manage to get your Sci slider up to about 40% without going broke.

What you NEED is a Great Merchant. Send him on a trade mission to a far away rivals city to generate a large amount of cash. I've had as much as 7500 gold come from one of these missions, and with that much, you can jack the science slider up to 100% for long enough to regain (or gain) a Tech lead. I've used this to win games.

The other thing that I'm starting to think about more is timing the production of Great People who can research Techs. Making an academy may give you an extra 75 beakers per turn for the next 300 turns of the game = 22,500 total long-term beakers BUT! wouldn't you rather WIN the game in a mere 150 turns instead! Using that Great Scientist to get a Tech that would have taken you 30 turns in one turn MIGHT be the better immediate use. Potentially same thing for all the others. Engineers in particular I think are pretty worthless to add to cities. You do not have the capacity to have multiple engineers in a city until the Industrial age, so your ability to generate them in the first 3/4 of the game is pretty limited and frankly random. I think a better use for them is to either rush Wonders, or discover Techs.

I'm also tending to think that the "Create Great Work of Art" thing is not such a generally great use for artists, and I'm wondering if adding the artists to a city does not increase the rate of Great Artist production. If one could get a city that is a Great Artist factory fairly early in the game, a Culture win is pretty much a foregone conclusion.

What's nice is the +100% GP point bonus in a golden age, in my last game I had a philosophical leader, I was in pacifism and when in the GA's I had +300% in all cities! with the national epic and Parthenon on top and a few cities as ULTIMATE GP farms... well, it got silly! I like to use great people for pretty much every purpose, whatever seems most apt at the time, and if I can't see anything I stick them in a golden age and speed up the conveyor belt for more!!

NC is right about the no bonus for GPs in cities.

Oh and I agree, in general, making a great work somewhere isn't such a great use but, when you have a specific city crying out for one it's GREAT. Some place in a vital border location as either offensive or defensive culture! Or if you've got multiple works it can do good in speeding up a culture victory.