To get to Tanzania, Airlines that fly to:

KILIMANJARO INTERNATIONAL AIRPORT:
Ethiopian Airlines, KLM, Kenya Airways, Condor, UT Air, Rwandair Express,

DAR ES SALAAM INTERNATIONAL AIRPORT:
Ethiopian Airlines, KLM, Emirates, BA, SAA, Qatar Airways, Air France, Lufthansa, Continental Airlines, Delta, American Airlines, Air Zimbabwe, Air Malawi, Swiss Air, Egypt Air

ZANZIBAR INTERNATIONAL AIRPORT:
Precision Air, Kenya Airways, Condor, Fly 540, Ethiopian airlines, KLM, Eurofly, Kitty Hawk

Or

If you opt to fly into NAIROBI, Kenya, you can then connect with local airlines to Kilimanjaro or Dar es Salaam or Zanzibar

The following Domestic Airline companies operate in Tanzania and some operate to Kenya as well:-

Regional Air
www.regionaltanzania.com

Precision Air
www.precisionairtz.com  

Coastal Air
www.coastal.cc

Zan Air
www.zanair.com

Air Excel
www.airexcelonline.com

Fly 540
www.fly540.com