I agree with most of the points Eugene made on this subject in his posts below. In particular, it's important to remember 1) that many other valuable institutions also have important downsides, and 2) that even if we need a strong federal role for the protection of certain kinds of minority rights, that does not mean we should have unlimited federal power over all or most other policies.
I would like to add three points to Eugene's analysis:
I. The Feds are Tainted Too.
There is no question that state governments have often oppressed minorities, particularly African-Americans. On the other hand, the federal government also has a far from perfect record in this area. Consider, for example, the federal internment of Japanese-Americans during World War II, and the feds' decades-long persecution of the Mormons during the nineteenth century. The states are "tainted" by their history, but so too is the federal government. Perhaps one can argue that the states are "more" tainted because they supported slavery, the single biggest human rights violation in American history. However, the federal government also played an important role in promoting slavery, for example through its enforcement of the Fugitive Slave Acts. If the history of state repression of minorities taints the argument for federalism, then the history of federal government repression taints the case for unlimited federal power.
II. Federalism vs. States' Rights.
There are important differences between the system of federalism advocated by modern scholars sympathetic to limits on federal power and the system of "states' rights" associated with the southern states' defense of slavery and later Jim Crow. The differences in are covered in some detail in my 2004 article "Federalism vs. States' Rights," (with John McGinnis). Perhaps the most important is the fact that an effective system of federalism requires citizen mobility between states, so that people can "vote with their feet" against jurisdictions that adopt harmful or oppressive policies toward them. This implies the need to prevent states from adopting policies that restrict interstate mobility and in effect hold people hostage. Obviously, slavery is a clear example of such a policy and Jim Crow also included efforts (such as peonage laws) to restrict black mobility. In addition, a well-functioning system of decentralized federalism requires limits on the power of states to assert an extraterritorial reach for their laws; otherwise, it would never be possible to vote with your feet against a particular state's legal regime. This point, too, has important implications for the history of slavery and Jim Crow, as southern states sought to assert an extraterritorial reach for their laws restricting the rights of blacks (e.g. - the Fugitive Slave Clause).
To the extent that modern defenders of federalism agree (as most do) that states must be prevented from restricting their citizens' mobility and from (in many cases) applying their laws extraterritorially, they are arguing for a very different system than that defended by the southern states in the eras of slavery and Jim Crow.
III. Reassessing the History of Minority Rights in America.
The claim that the history of slavery and Jim Crow "proves" that federalism is bad for minorities greatly oversimplifies the actually history of minority rights in the United States. It is certainly true that there were two periods in our history (roughly 1860-80, and 1940-70) when states' rights claims were used to counter federal efforts to protect the rights of African-Americans against abuse by state governments. To the extent that such efforts were successful, they certainly represent an important cost of federalism.
However, the conventional story that federalism is bad for minority rights overlooks other, at least equally lengthy, periods in American history when a unitary federal policy would have been worse for minority rights than federalism. At the time of the Founding, a unitary policy on slavery would probably have meant a requirement that slavery be legal all around the nation, since all thirteen original states had legal slavery. During most of the antebellum period (roughly 1790-1860) proslavery forces had much more power in Congress and the executive branch than antislavery ones, and a unitary policy on slavery and/or the rights of free blacks at that time would probably meant a compromise far closer to the slave state laws of the day than the free state ones. In those areas where the federal government did have authority, it tended to use it to promote slavery more than to restrict it. For example, the federal government facilitated the recovery of escaped slaves through a series of Fugitive Slave Acts (which some northern states resisted on "states' rights" grounds), and slavery was legal in the federally ruled District of Columbia until 1862. Indeed, the election of Lincoln in 1860 was important precisely because it represented the first time in decades that the presidency and Congress were both largely controlled by a (relatively) antislavery party.
During the post-Reconstruction Jim Crow era (roughly 1880-1940), a unitary policy on black rights would also probably have left blacks worse off than they were under federalism. At that time, southern whites cared far more about keeping blacks down than most northern whites cared about protecting their rights (and a significant minority of northern whites actually endorsed the southern position). Therefore, a unitary federal policy on black rights during this time would likely have led to a system slightly less restrictive than that which existed in the South, but far more oppressive than that which existed in northern and western states. At the very least, northern blacks, like southern ones, would probably have been denied the right to vote. The absence of relatively more favorable policies in northern states would have prevented blacks from "voting with their feet" against the South, an option that millions took advantage of from about 1900 to 1960; moreover, if blacks could not vote in the North, the incentive of northern white politicians to support federal intervention against Jim Crow would have been greatly diminished, and the landmark federal civil rights legislation of the 1960s might not have come as soon as it did.
Today, it is far from clear whether African-Americans are better off with more federal power or less. Arguably, black voters have greater power over many state and local governments where they form a large proportion of the population than they do over Congress. But even if African-Americans are, on net, better off with a more powerful federal government, that is not necessarily true of other minorities. Gays and lesbians, for example, benefit greatly from federalism and decentralization, as Albany Law School Professor Stephen Clark shows in this article (see also my own analysis here).
Ultimately, both state and federal governments can threaten the rights of minorities. Therefore, neither should be allowed unlimited power. The history of slavery and Jim Crow does not provide a clear case for either state or federal power. Both levels of government can repress minorities, and both need to be constrained.
UPDATE: Some commenters question my argument that a unitary federal policy on race in the post-Reconstruction era (roughly 1880-1940) would have been worse for African-Americans than federalism. Some of the historical issues involved are too complex to fully address here (though I make brief comments of my own in the notes). But the best window we have on what a unitary national policy on race would have been during this era is the way that federal government of that period addressed racial issues in those policy areas that were incontestably under its control. For example, the District of Columbia was under complete congressional control, and it had the same kinds of Jim Crow policies as the South (with congressional approval). The federal civil service was officially segregated under the Wilson Administration in the 1910s, and remained so under later Republican administrations. Federal immigration policy barred most nonwhite immigrants from entering the country under the Chinese Exclusion Act, the "Gentlemen's Agreement" barring Japanese immigration, and other related legislation. Finally, federal control in overseas territories such as Puerto Rico, the Virgin Islands, and others, did not exactly result in enlightened racial policies there (though full-blown Jim Crow could not be imposed because of the small size of the white population in those areas). We cannot know with certainty what the feds would have done had they had more power over racial issues during that era. But, based on their record, it seems likely that they would have done more to promote Jim Crow than undermine it.
UPDATE #2: I should note that I was slightly off in my statement that every state in the Union was a slave state at the time of the Founding (1787). The state of Massachusetts had abolished slavery by judicial fiat in 1783. Several other northern states had enacted laws mandating gradual emancipation of slaves, though most of them still had substantial slave populations as of 1787 and for years thereafter. On the other hand, two of the largest and politically most powerful northern states - New York and New Jersey - did not enact emancipation laws until 1799 (NY) and 1804 (NJ) respectively. In many of the other northern states, emancipation was deliberately made gradual so that slaveowners had a window of opportunity to sell their slaves "down the river" to the South, and thereby avoid the creation of a substantial free black population. Thus, my key point that, in 1787, a unitary national rule on slavery would have probably resulted in nationwide slavery is correct. All but one state was still a slave state; the majority had not enacted any emancipation laws; and many of those that had enacted gradual emancipation laws might not have done so absent the option of selling their slaves down South. Nonetheless, the facts are more complex than I indicated in the initial post, so I want to make sure to correct the mistake. For detailed information on the timing and structure of emancipation in the North (including the facts cited above) see this website.