Most nationalities require a visa to enter Tanzania. Arriving on a business visa is recommended but visiting crews also enter the country on tourist visas. Most nationalities can obtain tourist visas on arrival at the port of entry. Proof of yellow fever vaccination may be asked for if arriving from affected countries. See here for more information on visas to Tanzania.
Tanzania has an agreement with Kenya and Uganda to waiver visa re-entry fees if travelling between the three countries.
Visa and other entry and exit conditions (such as currency, customs and quarantine regulations) can change regularly. Contact your local Tanzanian embassy or representative for the latest information.