Its so simple to answer the thread's title,
They play like a team with Positive attitude, aggressive cricket, with complete determination/commitments whatsoever the situation may be and win like a team.
" Champion always do the things in different ways! ". Thats it.
Just for example, If we take India-Australia last series, there was no complete 100% commitments towards the game from Indian side like Dravid playing for some name sake... RP Singh running and delivering something so called that white ball while bowling
etc etc.
I remember the commentator saying, " If you are gonna beat these World Champs(Aussies), you have to give more than 100% through out these 100 Overs. Its not enough if you outclass them just for a while alone." ( when we lost one of the ODIs chasing > 300 ).
I would say, SouthAfrica and SriLanka next to Aussies because they also more or less play like a team almost in every game. If each and every player gives more than his 100% best(team effort), then we can have many Australian sides in cricket.