TransferWise serves over 300 transfer routes. You can learn more about the countries TransferWise supports here.
It depends on the country you're sending money to. In the Eurozone, you'll always need an IBAN and a SWIFT / BIC code. Banks in the USA use SWIFT codes, but they don't use IBANs. It's the same in New Zealand too. Learn more about IBAN numbers here.
As of today, 35 countries in the extended Eurozone are within the SEPA (Single Euro Payments Area) - including the United Kingdom, Switzerland and Germany. Learn more about which countries are in SEPA here.