FairGroundsRaceCourse.com has a Results Archive option on the menu under the Racing tab. Clicking on this option opens a link to the online archives at Equibase.com, which include Fair Grounds results for racing days since 1991.
Most race tracks post results for the current day's card racing at their websites. For historical cards, Equibase.com has a searchable database that includes cards for most North American tracks. For video coverage of stakes, allowance, maiden special weight and some maiden claiming races, BloodHorse.com offers another option at its website under the Race Videos option on the drop-down menu under the Multimedia tab.