A few, but only a few, words on two 19th-century philosophers: Jeremy Bentham and his disciple, who went off in his own, individual direction, John Stuart Mill. Both were utilitarians, and believed in the moral principle: "the greatest happiness for the greatest number." But they understood "happiness" differently. Bentham took it hedonistically: happiness (the good, the summum bonum) is pleasure. Sexual pleasure is a paradigm of the good in this sense: exquisite and exhilarating sensations. There are others: eating, sleeping, playing sports--all fun things. Mill thought that there were lower and higher pleasures: bodily, sensual pleasures, and the pleasures of the mind. These include, for example, reading a poem and enjoying its beauty. For Bentham, "pushpin is as good as poetry," that poetry was good only when and because it could produce sensations similar in kind to the bodily. Not so for Mill, who thought that these pleasures were qualitatively different (and only those who experienced both kinds could pronounce on their relative value). Mill thought that a full human life, one that exhibited what flourishing is for a human, would include both kinds of happinesses. He also thought: it is better to be a philosopher [Socrates] dissatisfied [grouchy, in part] than a pig satisfied. I still haven't decided whether Mill was right about that. Philosophers would tend to say such a thing, wouldn't they?
The answer to this question will depend on your conception ofhappiness. Not only do different philosophers differ in their viewabout what constitutes happiness (go here),they also have different views about how much of anything thatcontributes to happiness is required before one counts as happy. Thinkabout it this way. On different philosophical conceptions, differentthings count as good or bad for us. To the extent that we have the goodthings, we are better off. To the extent that we lack the good thingsand possess the bad things, we are less well-off. On a scale from very,very badly off to very, very well-off, there is a point at which onecounts as happy or eudaimon– namely, when one has enough ofwhat is good (and lacks enough of what is bad) to count as living a good life (that is, good foroneself), or as flourishing. Depending on how high on the scale oneplaces happiness and depending on the difficulty of achieving theconstituents of happiness, it will be more or less easy to becomehappy. If one sets the bar extremely high or if the constituents ofhappiness are extremely rare and difficult to attain, then it may wellbe impossible for humans ever to be happy; they can merelyapproach happiness.
It might be that every sane human being prefers their own happiness over their own misery; alas it doesn't follow from this that every sane human being always prefers other people's happiness over those people's misery. This comes to the crunch if promoting other people's happiness interferes with promoting my own happiness.