Nigeria and South Africa have recently signed a deal which states that holders of "official and diplomatic" passports are allowed visa-free travel between the two countries.
This agreement was signed by both Jacob Zuma and Goodluck Jonathan.
For the rest, visa applications are still required.
Countries that Nigerians can travel to visa free include:
Liberia, Mali, Mauritania, Benin, Burkina Faso, Guinea-Bissau, Niger, Senegal, Seychelles, Saint Kitts and Nevis, Turks and Caicos Islands, Cook Islands, Fiji, Micronesia, Nauru, Niue, Palau, Cameroon, Chad, Côte d'Ivoire, Gambia, Ghana, Barbados, Dominica, Grenada, Haiti, Montserrat, Samoa, Tuvalu, Vanuatu, and Kosovo.Sierra Leone, Togo, Cape Verde.
For further information, I would recommend getting in touch with the the official representative of South African visa related matters in Nigeria: The VFS Global it seems.... Here's there webpage: Vfsglobal.com/southafrica/nigeria/disclaimer.html
Good luck on your travels my friends!