There are many good reasons available for supporting the implementation of a universal basic income in our society, but I think most of them can understood in terms of promoting real freedom. A guaranteed income would boost people's opportunities in life, in a variety of ways.
Firstly, it would help relieve poverty. (As my first post on the UBI argued, it would likely be more successful than our existing methods of conditional/targeted welfare benefits.) Allowing people to meet their basic needs is an essential prerequisite to any form of freedom worth having. It would expand the quantity and quality of opportunities open to people, enabling them to live the sorts of lives they want to live. It would, in short, benefit humanity and promote one of the most fundamentally important values that there is.
Second, as discussed in my economy post, the UBI would increase the bargaining power of the worst off. Less desperation would leave people less vulnerable to exploitation. This in turn would relieve the need for many labour regulations. As I wrote before: We could realize the ideal of a genuinely free market, in which all participants - and not only the rich ones - can voluntarily participate.
Relatedly, the UBI would increase the market options open to individuals. It would, for example, enable people to work for less than a subsistence wage. This would make it easier for poorer people to find a job (as opponents of minimum wage laws are quick to point out). It would allow more people to accept more satisfying, if less well-paid, employment. It would also prevent people from being forced into accepting work that they greatly dislike. The most unpleasant jobs would thus have to offer greater compensation in order to entice people to accept them. This is only fair: people should be adequately compensated for performing distasteful jobs, they should not be forced into them from desperation. The guaranteed income would allow people to live for periods without employment, e.g. while they study or otherwise upgrade their skills. It would enable people to work more or less as they prefer. As Van Parijs notes, "access to an income, access to a job and access to leisure are all dimensions that must be taken into account when discussing justice." The UBI, unlike traditional welfare methods, and very unlike laissez faire capitalism, would offer greater access to all three.
It also has broader implications for social justice. Feminists argue that it would enable women to become less dependent on their husbands. Civil (little-'r') republicans point out that it would benefit democracy, by enabling more people to participate in public life. (If you're struggling just to survive, that doesn't leave you much time to get involved in politics or civil society.)
The most controversial aspect of the UBI, if high enough to meet people's basic needs, is that it provides individuals with the option not to work at all. This would seem to violate the reciprocity principle: if an individual takes from society, they have an obligation to give something back if they are able. But we should distinguish a moral obligation from its enforcement. I would agree that we do indeed have such an obligation, but its political enforcement might do more harm than good.
I discussed this more in my original UBI post. There are two main points to make. Firstly, valuable social contributions need not be economic in nature. Our present system woefully undervalues caring work (done predominantly by women) - especially the vital importance of childrearing - and other volunteer work done in service to civil society. Secondly, I think very few people would live lives that contribute nothing to society in this broader sense. Humans are social animals, and most of us want to do make something of our lives, whether through a successful career, or fulfilling some vital role in our communities. So I don't believe reciprocity would pose much of a problem in practice. What do you think?