Wiktionary has a potentially very cool page (http://en.wiktionary.org/wiki/Category:Etymology), where you can look for words originating from various languages. It's still under construction, and is probably years away from being a really useful resource. But even at this early stage, one thing jumps out at you.
Africa isn't sharing its words!
Most English words come from Latin, Greek, and Germanic languages. You can also find lots of words from various Indian languages (pundit, sari, ginger, karma, etc), North and South American languages (cocoa, chocolate, tomato, coyote, serape, chili, tamale, hooch, etc., etc.), and Asian languages (chow, judo, kumquat, ginseng, silk, Zen, kamikaze, futon, tofu, manga, ketchup, tycoon, soy, etc., etc., etc., etc.)1. Australia Aboriginal languages gave us fewer (boomerang, dingo, billabong, kiwi, etc.), mostly names of local plants and animals.
Africa, especially Sub-Sahara Africa2, despite having been known and explored for thousands of years, has not given us nearly so many words as the Native Americans, discovered only five centuries ago. There seems to be much less sharing of language than you would expect, even given the comparative lack of industrial societies in ancient Africa (and therefore less trade) and the rather drastic and one-sided cultural exchange between the Africans and Europeans. Much the same conditions were present in the New World, and the Europeans didn't hesitate to assimilate native languages while they were pillaging the Americas.
Like Australia, most of the words we've gotten from Africa are the names of animals and plants, although many of the best known African animals are not African words at all: hippopotamus comes from Greek, meaning "riverhorse"; elephant probably derives from some Indian or Phoenician word; rhinoceros is again from Greek, rhinokeros, meaning "nose horn"; cheetah is of Sanskrit origin; and 'hyena' is derived from the Greek word for a female pig, hyaina. Many 'African' words are actually Afrikaans words, deriving originally from Dutch (aardvark, aardwolf, meerkat, wildebeest, steenbok, roebuck/reebok, veldt). Thus far, the only Afrikaans word I've found that is both in common English usage and that is likely of native African origin is quagga.
So here the words that Native African languages have given us:
Animals: chimpanzee (Bantu), giraffe (?, probably came into Arabic (zarafa) from an African language), okapi (Mbuba), impala, (Zulu), gnu (Khoisan), macaque (Bantu), mandrill (?), mamba (Zulu or Swahili), quagga (Khoisan?), tsetse (Bantu), and zebra (prob. Congolese or Amharic).
Plants: yam (Fulani or Twi?), banana (Wolof?), okra (Akan?), goober (Bantu?), baobab (?), raffia (Malagasy), and cola (various).
Others: zombie (?), voodoo (?), dengue (Swahili?), dashiki (?), jukebox/jook house ('juke', Wolof and Bambara), bongo (Lokele?), marimba (Bantu?), djembe (Mandé), tango (an unidentified Niger-Congo language, maybe Ibibio), donga (Nguni), and, of course, Ubuntu! (Bantu).
Possibilities: They may have also given us mumbo jumbo, jumbo, gumbo, jive (Wolof?), boogie, jazz/jism (both probably of the same root, perhaps from Mandingo or Temne), banjo, conga, tote, chigger, gorilla, caiman, civet, and guinea, although these are less certain.
I'm still looking for more, and I'd love your help. I'm trying to keep to the relatively common words (that is, words that at least 10% of any given non-African English speaking country would recognize). I've left out words like tanzanite, boma, buckra, impi, obeah, and waragi as too obscure. If you have others, /msg me!
Here are some words that were not originally African: bwana and safari (used in Swahili, but originally Arabic); commando, commandeer (yes, used in Afrikaans, but from Portuguese and French roots, and from Latin roots before that); and savannah, an Arawakan Indian word (from the Taino tribe, to be specific), from the West Indies.
1. When reading through these words, you may find some unlikely claims -- ketchup being a Chinese word is probably my favorite. Well, with etymology nothing is certain, and I can't promise that all of these are true, and I can promise that many are misleading. For example, we don't really know where the word serape came from, but it's a good bet that it comes from a Nahuatl word, corrupted in pronunciation by Spanish speaking Mexicans. We do know that ketchup comes from the Chinese koechiap, meaning "the brine of fish." It changed meanings, and recipes, many times before becoming popular in its current tomato-based form. Language evolves constantly, which is what makes it so cool. I have done my best to keep all claims within the range of reason and supported by at least one source that I trust. If you think something looks wrong, look it up!
2. When I think of Africa, I think of Sub-Saharan Africa. There are Super-Saharan countries of course. If you are a fan of these, you may be interested in the following.
Egyptian (Coptic) words include: adobe, ammonia, ammonite, barge, gum, ibis, oasis, paper and papyrus, Pharaoh, and of course various gods (Horus, Thoth, Osiris). Alabaster, ebony, ivory, almanac, bible, basalt, and behemoth may also come to us from Coptic.
Keep in mind that most of these words have come to us from Coptic through Greek, Latin, French, and finally English. It is a long journey, and there are many words that may have come from ancient Egypt, but we don't have the resources to reliably trace them that far back. There are a few words that have come to us from Egypt more recently, for example loofah (Egyptian Arabic) and ankh.
Morocco gave us fez and tangerine.
Ethiopia helped give rise to the word Rastafarian (only partially Amharic, down a long and twisted path), and possibly zebra.
Ancient Carthage (where they spoke Punic) gave us Map. Mat and gorilla may also be Punic.
Thanks to Apollyon, General Wesc, StrawberryFrog, and Junkill for their additions.
http://www.krysstal.com/borrow/display_borrowtype.php?continent=Africa (not to be trusted!)