New to the exchange, please be gentle.
Are there any branches of philosophy that hold freedom as something that is intrinsically good? I think that libertarianism and various versions comprise one such branch, but are there any others?
It is best to set out some account of 'libertarianism', since until we have settled roughly what we mean by it, we can hardly tell what alternatives might also 'hold freedom as something that is intrinsically good'. We can't say what an alternative to libertarianism might be until we are clear what we take libertarianism itself to be.
Stephen Perry's account is broadly reliable :
Libertarianism is a moral and political theory about, among other things, justice in holdings. One of its central theses is, very roughly, that people are entitled to the fruits of their labor. Let me refer to this as the entitlement thesis. The entitlement thesis means that, for the libertarian, forced redistribution by the state (or by anyone else) cannot in general be justified; persons may only be required, at most, to contribute an appropriate share to the maintenance of a night-watchman state, the sole function of which is to keep individuals from violating one another's rights. The individual rights that libertarians recognize are rights to acquire property in specified ways, together with negative rights not to be subject to certain kinds of interference by others; the paradigm instance of such interference is deliberate aggression. But libertarianism does not generally recognize positive rights to receive assistance from other persons. I may voluntarily choose to confer a benefit on you, but no one - neither you nor any third party - can force me to do so.
Libertarianism is thus, in part, a theory about what individuals are entitled to, and one of the things to which they are said to be entitled is the fruits of their labor. But, as some libertarian theorists have recognized, libertarianism is also a theory about individual responsibility. More precisely, it is a theory about individual responsibility for the harmful outcomes of one's actions. Let me refer to responsibilty thus understood as outcome-responsibility. The conception of outcome-responsibility that has been defended by libertarian legal theorists focuses on the notion of causation. In the case of harms that one causes to others, the standard libertarian view is that the harm-causer has a moral obligation to pay the victim compensation; in legal terms, he or she is to be held absolutely liable to the injured party. The correlative right of the victim to be compensated is not just a remedial incident of the negative rights that persons have not to be subject to interference, at least not if we take the paradigm of such rights to be the right to be free from deliberate aggression. The reason for this is that many instances of causing harm to others are not only unintentional but unforeseeable. Thus there can be no meaningful injunction not to cause harm to others that is analogous to the injunction not to engage in deliberate aggression against others. Similarly, there can be no ex ante duty, except in the most formal sense, not to cause harm to others, and accordingly no corresponding right not to be harmed. The primary duty is an ex post duty to pay compensation after harm has occurred, and the corresponding right is a right to receive the compensation. The libertarian conception of outcome-responsibility is, in the case of harm that has been caused to another person, essentially co-extensive with this duty.
(Stephen R. Perry, 'Libertarianism, Entitlement, and Responsibility', Philosophy & Public Affairs, Vol. 26, No. 4 (Autumn, 1997), pp. 351-396 : 351-2.)
There is a strong, defining, emphasis in libertarianism on entitlement to ownership, including the difficult notion of self-ownership. The state is more enemy than friend, a protector of entitled holdings and an enforcer of contracts and of the security without which ownership is impossible, but also a permanent and in contemporary polities increasingly menacing threat to entitled holdings through policies of redistribution of wealth.
It is a common view that libertarianism is a kind of liberalism. Liberalism, however, is a subtly different view. Freedom is an intrinsic value but different kinds of freedom are recognized besides freedom of (property) holdings and of contract and other values besides freedom and justice are vital parts of the liberal picture. It is, of course, pointless to try to define the essence of liberalism. Classical liberalism centres on formal rights; what might be called 'high liberalism' is concerned with substantial rights. (More on this under 'Equality of opportunity' below'.) But as it is widely understood in contemporary political discourse, liberalism can be specified under a number of headings :
The most characteristic feature of a liberal society is its toleration of beliefs and diverse ways of life. Dissent, nonconformity, and an assured space of independence are accepted as normal in social life. Toleration is institutionalized by the political recognition that certain liberties are more important than others. These basic liberties are designed to maintain, through the rule of law, the security and integrity of persons and their freedom to live as they choose, within prescribed limits. Basic liberties apply to all persons equally (or at least all citizens) without regard to social or economic status. The equality of basic liberties is the primary way that equality is recognized in liberal institutions. Liberal philosophers offer different lists of basic liberties, but for all of them liberty of conscience is centrally important. Liberty of conscience includes freedom of religious beliefs, which was critical to liberalism's origins in the seventeenth century. It has in modern times come to include freedom to form philosophical views and ethical con- victions about questions of ultimate value and life's meaning. Liberty of conscience is perhaps the most important liberal basic liberty since it secures toleration of religious, ethical, and philosophical beliefs and allows for pluralism of conceptions of the good. But other liberties have come to be regarded as of equal political significance. The list of liberties that Mill maintains as part of his Principle of Liberty are liberty of conscience; freedom of thought and discussion (including freedom of speech, press, and opinion, and inquiry into all subjects); "freedom of tastes and pursuits," or the freedom to pursue a "plan of life" to suit one's character; and freedom of association. Rawls's list of basic liberties is similar. In addition to liberty of conscience, freedom of thought, and freedom of association, Rawls includes equal political liberties (including the right to vote and hold office, freedom of assembly, and the right to organize and join political parties), the rights and liberties needed to maintain the freedom and physical and psychological integrity of the person (including freedom of occupation and of movement, and the right to hold personal property); and the rights and liberties needed to maintain the rule of law. (Samuel Freeman, 'Illiberal Libertarians: Why Libertarianism Is Not a Liberal View', Philosophy & Public Affairs, Vol. 30, No. 2 (Spring, 2001), pp. 105-151 : 108-9.)
▻ Equality of opportunity
A second feature of a liberal constitution is the absence of political restrictions on entry into social and political positions. Positions are to be held open to everyone regardless of their racial, ethnic, or gender group, religious or philosophical views, or social or economic position. Equal opportunity developed out of the rejection of the idea that people are assigned social positions by birth, and cannot legally move out of their class into another. As Kant said, "Every member of the commonwealth must be permitted to attain any degree of status ... to which his talent, his industry, and his luck may bring him; and his fellow subjects may not block his way by [appealing to] hereditary prerogatives." The requirement of open positions is part of equality of opportunity. This is another way that liberals incorporate equality, in addition to equality of basic rights.
Liberals interpret equality of opportunity differently. At a minimum, it is formally construed as an absence of legal or conventionally imposed restrictions that bar socially disfavored groups access to social positions. Discrimination in allocating positions that are based on race, gender, and other natural or social attributes unrelated to job performance would then be legally prohibitable. The underlying idea is that careers should be "open to talents" (as Adam Smith said) or to "merit" (as others say), that is, positions should be accessible to all who are willing to compete for them and who are able to satisfy performance demands. The "system of natural liberty" affirmed by classi- cal liberals incorporates this formal conception of equal opportunity. This reading fits well with classical liberals' emphasis on economic efficiency.
Other liberals contend that merely eliminating restrictions on entry to positions does not take equal opportunity seriously enough. The sense in which positions are open to the poor is nominal if not illusory under the formal conception, since the poor have no real opportunity (far less an equal or fair one) to compete for favorable positions without educational benefits. Society then has a duty to support an education system to even out class barriers so those with similar abilities can compete on an equal footing. Others argue that fairness requires still more, namely, both adequate universal health care so that all may realize their capacities, and preventing excessive accumulations of property and wealth. These fuller conceptions of equality of opportunity are characteristic of the high liberal tradition, and mark one major difference with classical liberalism. (Samuel Freeman, 'Illiberal Libertarians: Why Libertarianism Is Not a Liberal View', Philosophy & Public Affairs, Vol. 30, No. 2 (Spring, 2001), pp. 105-151 : 108-9 : 115-6.)
Liberalism an alternative to libertarianism
Other dimensions along which libertarianism and liberalism can be compared and contrasted are the reliance on markets and the provision of public goods. But enough has been said to mark out liberalism as a separate position, an alternative to libertarianism within the shared assumption of the intrinsic value of freedom.
To begin, liberalism is concerned with a wider range of freedoms than libertarianism. Does Nozick, for instance, even mention freedom of conscience ? More than that, recall Freedman's observation on behalf of 'high liberalism' :
The sense in which positions are open to the poor is nominal if not illusory under the formal conception, since the poor have no real opportunity (far less an equal or fair one) to compete for favorable positions without educational benefits. Society then has a duty to support an education system to even out class barriers so those with similar abilities can compete on an equal footing. Others argue that fairness requires still more, namely, both adequate universal health care so that all may realize their capacities, and preventing excessive accumulations of property and wealth. These fuller conceptions of equality of opportunity are characteristic of the high liberal tradition.
If we take this view of the requirements for equality of opportunity then we are plainly committed to the legitimacy of state redistribution of wealth to turn formal equality into substantive equality - equality in the real world and not merely on paper.
I take no side in this dispute. But liberalism as here described is plainly discrepant from libertarianism while equally recognizing the intrinsic value of freedom. It is a genuine alternative to libertarianism.
Regarding Sartre (mentioned by “Gordon”): freedom is central to his philosophy. But his understanding of freedom is very strange (to the point of him claiming that no normal human can fail to be free), so that's probably not what you're looking for.
You mentioned libertarianism and this is a good place to start. But since for mainstream libertarian thought, "freedom" is extremely tightly connected to property, it's probably more rewarding to look at “heterodox” libertarians (e.g. Benjamin Tucker, Henry George).
One very interesting article is “Freedom and Property: Where They Conflict” by Frank van Dun (ironically hosted by the Mises Institute), which IMHO seems to be a good vaccine against falling into the trap of understanding freedom in a too “property-focused” way (though, admittedly, orthodox libertarianism is probably the only philosophy which managed to define freedom in a not obviously inconsistent manner).