The jester is a total waste of money - ends up where you spend 700 gold to get 20 happiness when he's 'perfected' his routine.
The circus is always good
The vampire's mystic ball is sometimes good but usually not, being spooky costs you a population for no gain, accepting the nickname gains 1 happiness.
The mage's magic is sometimes bad but usually good.
I paid off the dragon one time, I would guess if you don't you lose a large amount of population. Later I was able to send someone to kill him and got a large reward from it
The gold machine works but only gives minimal amounts (with occasional slightly larger amounts). I would suggest paying the scientists for the initial investment but not giving them further amounts. The machine will eventually be completed.
The music machine was a bust. It made people unhappy and eventually had to be removed. The potions killed people. However, I don't know if you turn them down if that stops the scientists from offering other better things. I also don't know if there is a randomized result where sometimes they are good.
The foreign investment guy who offers a deal for our 'tiny, little town' mostly gives bad deals that aren't worth it. The only one I've found good and that I accept is the trade mission.
Appeasing the spirits - not sure if this worth it. It's 200 gold to keep them appeased. It's 1000 gold later if you turned down all the 200 gold requests. I didn't count how many 200 gold requests I ignored before the spirits needed to be appeased - if it's more than 5 then it would be worth it to ignore them, Otherwise the 200 gold installments is the better value.
So far paying gold to the ocean shrine has gotten me nothing. It might be like the spirits though with something big bad happening eventually.
I accepted the plant people and that has been totally good. As is accepting people from other dimensions. Pretty much any offer to accept people has been good.
In the dispute between kingdoms I sided with the plant kingdom and that had a net positive effect. I would be interested in hearing what happened for anyone that sides with the ocean people. It may be that siding with the plant kingdom is what caused plant people to grow in the kingdom.
I play the good guy. So I don't allow the thief to steal and that's worked for me. I also don't make any deals with the devil or sacrifice people.
I always allow the barber to raise his prices and that's been good. Same for giving the butler time off.
When the chest eats people (even though he's been told not to) I take the gold . Not taking the gold gives you nothing and doesn't avoid population loss.