For reasons disturbingly easy to understand, African-American family history research can be extremely difficult, especially as one ventures back more than just a few generations. Researching slave history is a special challenge. But there are a few online resources available that allow one to at least begin the quest.
The Trans-Atlantic Slave Trade Database includes more than 67,000 Africans brought (or should I say bought!) to America aboard slave ships. There are various searches possible here, focusing on individuals, identified by name, gender, place of origin, and so on, as well as on particular voyages or slaving expeditions.
The online database, Afro-Louisiana History and Genealogy: 1719-1820, is a remarkable piece of work, essentially put together by a single researcher, Dr. Gwendolyn Midlo Hall, a professor of history at Rutgers University. There are records here of about 100,000 slaves brought to (or through) Louisiana in the 18th and early 19th centuries. The French and Spanish slave traders and owners apparently kept far more meticulous records than did their counterparts in the East, leaving a wealth of information for historians.
The entire dataset can be searched online, but if you're handy with databases, SQL, SPSS, and things of that sort, you can download two large files to work with on your own: a Slaves Database, and a Free (ex-slaves) Database.
The Illinois Servitude and Emancipation Records Database, 1722–1863 is a small but significant collection dating back to colonial Illinois. About 3,400 slaves and slave holders are listed here, and the state will provide copies of original records, if requested.
Indiana's Digital Archives include countywide Negro and Mulatto Registers from 1853, and the Clark County Slave Register of 1805. At the site, click on Misc Historical Records for more details about these collections.
Maryland's Online Archives include several slavery-related lookups, including general and slave censuses, records of runaways, slave jail records, and pardons issued.
I also want to mention the very worthwhile, but very frustrating African-American collections at the Archival Research Catalog (ARC), a division of the National Archives. There is a lot of material here. But, it is a difficult site to search and make sense of results, and more often than not, you will be pointed to off-line sources of information, rather than being able to access materials online. Still, it is a rich resource, and worth the effort. Make sure to do a general search of ARC in addition to browsing the African American collection. Try a search on slaves, and another on slavery, to see what turns up.
You can find free online newspaper archives at the Special Collections page of FreeNewspaperArchives, related to slavery, the Civil War, and abolition.
Lastly, I recommend this excellent article on Why Retracing Our African Roots is So Difficult.
Visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.
And don't forget to also check for your family history at Ancestry.com and NewspaperArchive.com. These are subscription databases, but they are among the most powerful research tools available for looking into family roots.