I would say there are three parts to answering that question: how many to get during lane phase, how many to get later in the game, and how aggressive is the other team about clearing your wards. The minimum is enough that you are never killed by someone who did not get spotted as they approached. Beyond that it is about having information to make better strategic decisions.
As mid lane the minimum I feel is needed to do more that farm creeps on my side of the river is to have vision of the river on both sides. Usually I place my pink in the bush between the cliff and the wall behind blue buff. Then a green in the lonely bush in the river on red buff side. Ideally I also place a green near the enemy turret to see if they roam, back, or in the case of TF ult (with him this ward is more important). The final green ward if I have a third it goes in the bush near the enemy wraiths to see when their jungle is passing through / doing wraiths (if I am pushed and have a good wave clear spell like Morgana's Tormented Soil while they are doing them I will some times throw it down to try and snag them while the jungle is farming them).
As support I put out lots of ward everywhere. During lane phase after getting a sight stone I ward the blue side tri-bush (often a pink if on blue team), river/dragon, and the lane bush.
As adc I pink ward the bush near the bot side buff for my team.
Late game in all positions that I do not get a sight stone in, I always drop a pink on baron if I do not trust my team to keep vision on it. If I have a sight stone I use that to keep vision of baron.