A short article by Don Peck and Ross Douthat in The Atlantic Monthly summarizes some research on the relationship between income and happiness by Dutch sociologist Ruut Veenhoven. Peck and Douthat interpret the results as suggesting that

Above about $20,000 per capita, increases in wealth yield at best minimal increases in happiness.

They must mean “income,” not “wealth.”
More important, economists are automatically skeptical about this sort of research. The fact that people choose to earn more than $20,000 in income strongly suggests that higher income produces more happiness. When what people do in the market contradicts what they say in a survey, economic empiricists tend to view the market decision as more indicative. The formal term we use is revealed preference.