The large and diverse continents of Africa and Asia present a challenge for anyone attempting to research African or Asian family history. Very few records are available online. The Internet can still provide a great research tool for learning about the history of the area where your ancestors once lived and for connecting to other genealogists with research interests in the area.
AfriGeneas (www.afrigeneas.com) is the largest jumping-off point for Americans looking to trace their roots back to Africa, with records, forums, and mailing lists devoted to helping you connect your African American ancestors to their place of origin in Africa. Once you have at least identified your ancestor's country of origin in Africa, the AfricaGenWeb Project (www.africagenweb.org) may provide some assistance with directing your research efforts in Africa. If your ancestors were from South Africa, spend some time exploring the National Archives of South Africa (www.national.archives.gov.za), where you can search an index to several helpful databases. It is important to note that these are only indexes to available records. The actual documents will need to be requested from the Archives.
The AsiaGenWeb Project (www.worldgenweb.org/index.php/asiagenweb) includes links to a variety of country websites, covering a broad area from Turkmenistan in the west to East Timor in the east. Many of these sites are actually in need of hosts, and thus provide little in the way of useful information. The best include ChinaGenWeb (www.rootsweb.ancestry.com/~chnwgw) and JapanGenWeb (www.rootsweb.ancestry.com/~jpnwgw). For people tracing European ancestry in India, the Families in British India Society (www.fibis.org) provides a number of useful lists and databases. An interesting site for those with Korean ancestry is the Korean History Project (www.koreanhistoryproject.org). Yes, FamilySearch (www.familysearch.org) has some historical records online too, including vital records for India, Sri Lanka, and the Philippines.