In "The Matrix", Agent Smith explains to Morpheus that the original idea was to have humanity live in utopia... and it failed miserably because human beings expect hardship and turmoil. Given a perfect world, people immediately distrusted their environs. Only by creating an imperfect scenario where humanity was allowed to struggle did the plan work.
I don't think he was that far off, to be honest.
We as a species are competitive, but still very social, creatures. We take a sense of self-worth from our ability to overcome difficulty, as well as our ability to 'keep up with everyone else' as far as economic and social standards go. Competition causes an increase in ability for all concerned, and thus becomes not only a way of generating a 'standard', but of raising the bar for everyone. Four-minute mile, anyone?
Being happy isn't necessarily about having bigger or better toys, or luxurious vacations. Being happy is more about feeling that you are achieving your best personal potential, and are able to compete with those around you in a healthy way... and in our given society, having material things contributes greatly to that feeling. They are status symbols, like trophies, that prove we have overcome adversity and achieved something of value.
Those who, for whatever reason, are unable to achieve their potential according to societal standards tend to feel worthless, ashamed, and angry. These feelings can lead the underachiever to find other ways to 'succeed', by means of trickery or deceit, and thus they can feel that they're 'smarter' than those who struggle because they 'found a way to buck the system'.
IMHO, this is why welfare systems are not as successful as their originators intend them to be - because while they provide the basics, they typically do not provide the sense of accomplishment or ability to compete normally in the recipient. When someone else is providing for you, they are essentially taking your place in society and removing you as a viable person. Over time, this creates a cycle of dependency and resentment much like the 'growing pains' we experience as children. But if we're not able to grow out of that cycle, we stagnate and become stunted.
So... does money buy happiness? No. But the earning of money, specifically in amounts that allow us to compete with society to the standards we set for ourselves, can lead to a sense of fulfillment.