It depends upon which airlines you're travelling with.
The budget airlines operate on a 'point-to-point' basis. This means that each leg of the trip is regarded as a separate journey, so you have to claim your baggage and check-in again, even if you're flying with the same airline.
If you fly with the full-price carriers, they operate 'through ticketing' across different airlines. So if your flight, for example, is with BA from Heathrow to Singapore, and then with Qantas from Singapore to Sydney, you'll only need to check your baggage in at Heathrow and collect it at Sydney.
Chris