Considering that civilizations developed in other areas relatively quickly, South and central America for example, was there a reason it didn't happen in Sub Saharan Africa?
This has been asked before and there are probably a few answers that may be of interest in the FAQ.
So there's a couple of problems with the question that you've asked. The term civilization as a lot historians will claim is a loaded term. "Civilization" is a subjective term, people decide what they think civilization is. Its no coincidence that the areas considered most civilized are those that bear the most resemblance to Europe and European cultures an styles of rule. In the early days of colonialism civilization (or lack of) was used as an excuse to push imperialist policy such as the annexation of African states or polities. In this regard, it was in the interest of imperialist countries with colonial ambitions for there to be no 'civilization' in Africa. In many ways the definition of civilization deliberately excluded the pre-colonial African nations. So the reason we see very few "Civilizations" in Africa is that the definition of civilization was defined so as to exclude Africans.
However, If what you're asking is why there were no complicated polities and states in sub-Saharan Africa, then the simple answer is that there were. People have already mentioned the West African states of Ghana, Mali and Songhai. There has consistently been states in the horn of Africa such as Abyssinia/Ethiopia and Muslim coastal states dating back to the early 1000's. South of the horn there is the state of Buganda (in modern day Uganda) can be dated back to at least the 14th century. Towards the south of Africa societies such as the Nguni (the Zulu are included in this group) the Lunda, the Luba and the Tswana (to name a few) were all very complicated states and polities. Those are just a few of the states that existed in Africa prior to colonialism.
I dislike linking to wikipedia and there are certainly better sources out there but this gives a small idea about the variety of cultures and states in sub-Saharan Africa.
http://en.wikipedia.org/wiki/African_empires
If you're interested further, I'd suggest asking a question here (about a specific state or culture) or digging into the reading list.
http://www.reddit.com/r/AskHistorians/wiki/books/africa#wiki_general
hi! you may be interested in responses to these other posts
Why were there so few empires in Africa? - a quick list for reference
Were there any large African Empires?
How much do we now know about the Kingdom of Zimbabwe? Is this an active area of study?
A few questions pertaining to the mysterious Great Zimbabwe.
Why have there been so few Sub-Saharan African cities in pre-colonial history?
I just realized that perhaps /r/askanthropologists might be the better place to pose this question.