Use these resources from The World Bank:

• Migration and Remittances webpage, for data on bilateral flows from many countries
• Remittance Prices Worldwide

Use UNCTADstat for remittances back to 1980. Select Data Center, then Balance of Payments, then Personal remittances to open a configurable table.

Use Sage Data to retrieve data from The World Bank's World Development Indicators: 

• Select Browse Data by, then Source, then World Bank.
• Along the left, choose World Development Indicators, then Economic Policy and Debt.
• Scroll right (depending on your screen) to view the Socioeconomic Indicator box.
• Within this box, select a Personal remittances, paid or Personal remittances, received option.
• Select any relevant Year and Country options.

Look at the MPI (Migration Policy Institute) Data Hub, under Research & Initiatives, select Data, then International Data.

For remittances specific to the Western Hemisphere, use the Inter-American Development Bank.