Philosophy, etc considers the question of what are, or should be, the core values of left-wing thought? His answer is pretty much the same as mine: that it is about freedom, but a freedom that is substantive, rather than merely formal.
As Philosophy, etc notes, the right's conception of freedom is very "thin", and does not consider at all the question of whether such freedom can actually be exercised. It is also concerned only with freedom from state interference; it does not consider private individuals to be capable of limiting freedom (or else that such restraints do not matter). Combined, these render the right's conception of freedom nothing more than a cruel joke, leading to absurdities such as people still having "freedom of religion" even when some forms of worship result in private punishment no different from state oppression, or having "freedom of movement" even when they are forbidden to step out of their house and onto the privately-owned sidewalk. The only sort of "freedom" this is is freedom for the pike.
By contrast, the left's vision of freedom is one that can actually be exercised:
This means preventing the powerful from limiting other people's freedom (justifying employment law and anti-discrimination legislation), enabling people to make the most of themselves (hence state-provided (or at least regulated) education), and insulating them from the vagaries of fortune, of ill-health or poverty, so that they will be able to pursue their vision of the good (or at least not completely lose sight of it) regardless of circumstance (giving us social welfare and a comprehensive health system). In other words, your standard redistributive liberal-democratic welfare state, supported on the grounds that freedom is for everyone, not just the rich.
Those grounds point to a second left-wing value: equality. Historically, this has mostly been seen in the quest for (greater) economic equality, driven by the stunning inequalities of wealth and hence life-chances between rich and poor that were so graphicly displayed during the Ancien Regime and industrial revolution, but there are other strands as well. One is for equality of opportunity - for everyone to have a decent start in life and a chance to reveal their talents regardless of the circumstances of their birth. Another is moral equality - the equal valuing of all regardless of wealth or status. And these latter strands provide a modern justification for the former: to the extent that economic inequality interferes with either moral equality or equality of opportunity (or substantive freedom, for that matter) we are justified in limiting it (though ideally by raising the bottom rather than lowering the top).
Finally, I'd add democracy to the list. The belief in moral equality has led to a sustained effort to widen the circle of government and put power in the hands of the people. Even those strands of the left which took a markedly anti-democratic turn at least claimed to be attempting to do this (unfortunately, they were poisoned by their belief in false consciousness, the idea that people are deceived about where their "true interests" lie). And in the west, where Marxists have been less successful in seizing power, left-wingers have been consistent in their support of extending the franchise to the poor, to women, and to ethnic minorities.
This is of course a liberal conception of left-wing values, but I think it provides a far firmer ethical grounding than the traditional grounding in social class.