This graph on mean life satisfaction vs. per capita GDP is one of the most interesting poll results I've seen.
I don't think any of us needs Gallup to tell us that someone from Chad (a land-locked Central African country bordering Darfur) is likely to be less happy with his lot than a Dane. So, in that sense, yes, people in richer countries are happier than those in poor countries. But the relationship is by no means linear.
For example: Venezuelans, Saudis, Brits and Americans are all approximately equally happy with their lives, even though the average American is five times wealthier than a Venezuelan and twice as wealthy as the average Saudi.
Meanwhile, even though China, India and Pakistan all have approximately the same level of wealth, Pakistanis are much happier than Indians who in turn are much happier than the Chinese.
My hunch is that is also cultural. Islamic societies seem to be happier and Eastern European countries more dour than their incomes would suggest. Pacific Rim countries are happier the richer they are -- a nearly linear relationship holds amongst countries such as Korea, Japan and Taiwan.