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Jeremy Bentham and John Stuart Mill are counted among the classical utilitarians. They spoke in terms of pleasure, pain, and happiness. In their view, utilitarianism was based on the principle of utility, which requires us to act so as to produce the greatest total pleasure or happiness for human beings (or for all sentient creatures). 

The classical utilitarians were not 20th-century analytical philosophers. Their writings do not contain lengthy analyses of the concepts of good, right, ought, and so on. It is probably correct to say that they were not primarily moral philosophers at all. Bentham, for example, was mainly concerned with the reform of law and the modification of social institutions. Both men quoted here were passionate political activists devoted to social reforms. Nevertheless, their writings are considered definitive for early and mid-19th century utilitarianism.

Jeremy Bentham published the Principles of Morals and Legislation in 1789. He was not the first to put forward the principle of utility as the fundamental moral principle; but his long life, his extensive writings, and his constant involvement with plans for every kind of institutional reform helped make the principle of utility famous, influential, and controversial.

Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do. On the one hand the standard of right and wrong, on the other the chain of causes and effects, are fastened to their throne. The govern us in all we do, in all we say, in all we think: every effort we can make to throw off our subjection, will serve but to demonstrate and confirm it. In words a man may pretend to abjure their empire: but in reality he will remain subject to it all the while. The principle of utility recognizes this subjection, and assumes it for the foundation of that system, the object of which is to rear the fabric of felicity by the hands of reason and of law. Systems which attempt to question it, deal in sounds instead of sense, in caprice instead of reason, in darkness instead of light....

The principle of utility is the foundation of the present work: it will be proper therefore at the outset to give an explicit and determinate account of what is meant by it. By the principle of utility is meant that principle which approves or disapproves of every action whatsoever, according to the tendency which it appears to have to augment or diminish the happiness of the party whose interest is in question: or, what is the same thing in other words, to promote or to oppose that happiness. [Jeremy Bentham, The Principles of Morals and Legislation, Chapter one, Sections I and II]

John Stuart Mill first published his well known discussion of utilitarianism in three parts in Fraser's Magazine in 1861. It was later printed and many times reprinted as a short book. Mill provides the following statement of the doctrine:

The creed which accepts as the foundation of morals "utility" or the "greatest happiness principle" holds that actions are right in proportion as they tend to promote happiness; wrong as they tend to produce the reverse of happiness. By happiness is intended pleasure and the absence of pain; by unhappiness, pain and the privation of pleasure. To give a clear view of the moral standard set up by the theory, much more requires to be said; in particular, what things it includes in the ideas of pain and pleasure, and to what extent this is left an open question. But these supplementary explanations do not affect the theory of life on which this theory of morality is grounded -- namely, that pleasure and freedom from pain are the only things desirable as ends; and that all desirable things (which are as numerous in the utilitarian as in any other scheme) are desirable either for pleasure inherent in themselves or as means to the promotion of pleasure and the prevention of pain. [J. S. Mill, Utilitarianism, Bobbs Merrill, p. 10]

According to the greatest happiness principle, as above explained, the ultimate end, with reference to and for the sake of which al other things are desirable -- whether we are considering our own good or that of other people -- is an existence exempt as far as possible from pain, and as rich as possible in enjoyments, both in point of quantity and quality; the test of quality and the rule for measuring it against quantity being the preference felt by those who, in their opportunities of experience, to which must be added their habits of self-consciousness and self-observation, are best furnished with the means of comparison. This, being according to the utilitarian opinion the end of human action, is necessarily also the standard of morality, which may accordingly be defined "the rules and precepts for human conduct," by the observance of which an existence such as has been described might be, to the greatest extent possible, secured to all mankind; and not to them only, but, so far as the nature of things admits, to the whole sentient creation. [J. S. Mill, Utilitarianism, Bobbs Merrill, p. 16]
In more recent writing, utilitarianism has been made much more complex in order to meet a variety of objections. For example, in his article "Toward a Credible Form of Utilitarianism" Richard Brandt gave the following sketch of a more defensible form of the principle of utility.
The principle with which we end is this: "An act is right if and only if it conforms with that learnable set of rules the recognition of which as morally binding -- roughly at the time of the act -- by everyone in the society of the agent, except for the retention by individuals of already formed and decided moral convictions, would maximize intrinsic value."

For a clear account of 19th century utilitarianism and its critics, see J. B. Schneewind Sidgwick's Ethics and Victorian Moral Philosophy. Utilitarianism is placed in a larger intellectual context in Elie Halévy's unsurpassed work, The Growth of Philosophic Radicalism.