My girlfriend and I stayed in Zanzibar for two weeks in January 2013. In the beginning we got the hotel to call for taxis for us. Many of them were driving unsafe and often tried to push tours, etc. on us.
After a while we found a really good and reliable taxi driver. His name is Mwalim and he drives safe and charges decent prices.
His phone number is: +255773161230.
If you're going to Zanzibar and want a good taxi driver, we can really recommend Mwalim!