As milesofjazz already mentioned, we'd simply revert to the system of barter we had before there was a common currency. Overall, I don't think people would be happier, since most of the world seems to have forgotten how to produce many of the goods needed to sustain life, and because the growth and manufacture of all the essentials are so spread out now thanks to the structure of commerce that we have. For instance, my own skills are not in demand locally, but I'm still able to make a living off of them because people can send me money in payment for my services, and in turn I can buy food with that money. My clients in other countries can't just send me food for my services. Then again, most of the types of food available in my community comes from elsewhere because very little can grow here aside from corn, potatoes, wheat, and a few other such crops. If we want fruit, rice, and other such things, we'd have to come up with something that not only the people who have the food want, but also what the people transporting it want too...and it can't be available where they come from, because then they might as well just get it there.
Overall, we're really not set up for a barter system anymore, and without currency we'd have to completely rebuild our structure for production, manufacture, and trade...and the pursuit of a powerful bartering empire would no doubt consume the same people who are now consumed by the pursuit of money, because all money really is is a more versatile bartering tool. The greed that makes money a problem would still be there, so taking it away isn't what would fix the problem.