According to Friedrich Hayek, star of interwar economics, and recently star of two excellent rap battles with his contemporary John Maynard Keynes, the type of equality that matters is equality before the law. Equality before the law—and not equality of opportunity, outcome or anything else—is absolutely central to his political philosophy. But I think his economic work, particularly his crowning achievement, "The Use of Knowledge in Society" (cited a mere 9,496 times), points to the importance of a different kind of equality.
In "The Use of Knowledge in Society" and in earlier work in the socialist calculation debate Hayek shows that scientific knowledge isn't the totality of knowledge in society. In fact, a much bigger body of knowledge—information about peculiarities of time and place and preferences—is dispersed extremely widely across individuals. The only effective way of using this knowledge is a market system. Market participants act on the information embedded in different prices, and in doing so send yet more information back in other prices. But each participants learns only what she needs to know.
The market system Hayek envisions is a great practical means of organising society to achieve high social welfare. The flaw with this system is that participants with more money get to send stronger signals than others.
Markets measure how intensely we want things much more accurately than most democratic systems, because individuals have to bid against others for desirable goods or services. But this breaks down if individuals lack equal wealth. Ten pounds spent by a pauper is likely to represent a much more intense preference than that same £10 spent by a billionaire, a millionaire, or even the average middle class homeowner. However, producers will treat these £10s the same, and the economy will be skewed towards satisfying wealthier people's preferences.
Actually, it's not as simple as that. One feature of the market system is that people get rewarded with more money income (and potentially wealth) if they choose less leisure, or a riskier or less satisfying job. These sorts of inequalities, even if they produce wealth inequalities, would not subvert the system. These individuals have paid for their higher wealth with lower utility in work—and extra wealth merely evens out the overall extent to which the economic system is tilted to their advantage.
But endowments of talent or wealth through better upbringing, genetic advantage or inheritance do subvert the system, and undermine Hayek's argument for the efficiency and rationality of the market order by counting some people's preferences as more than one.
Now, by no means am I saying it's easy to disentangle these "good" sources of unequal wealth from the "bad" sources, or even that we ought to try to do so, and then even out endowments. But I do think that the effect inequality of wealth has on the market functions as a strong—and Hayekian—reason to desire a flatter distribution.