QuickBooks Desktop (US, UK & Canada):
Pro, Premier (all editions), Simple Start & Enterprise Solutions
See QuickBooks importing instructions here
MYOB Desktop (AU & NZ):
AccountRight v19 (Enterprise, Premier, Plus & Standard)
Accounting v18.5, Accounting Plus v18.5, Premier v12.5, Premier Enterprise v6.5
Accounting v18, Accounting Plus v18, Premier v12, Premier Enterprise v6
Accounting v17, Accounting Plus v17, Premier v11, Premier Enterprise v5
See MYOB importing instructions here
Other Accounting Software:
Fathom also let's you manually import data from any other accounting system via Excel.
See Excel importing instructions here