This will be republished as time goes on and more spelling differences are noted. If you add something in comments about a different spelling, I will add it to this post. We will start with the most obvious and the easiest.
Colour is the Australian spelling. Color is American. The spelling color is generally not used by Australians.
Labour in Oz. Labor in the US. The exception is the extraordinary decision by one of our two major political parties to change its spelling and call itself the Labor Party. Labour is generally used in Australia.
Satellite here, satelite in the US. This one did my head in because spell checker kept telling me it was satelite, but it just looked wrong. Speaking of double lls, labelling/labeling, towells towels. Hmm, towels, I am not sure about that. This is the problem of modern communication.
As I said, I will add to this list, but you could surprise me with one I don't know.
The ise/ize word ending
Gaol/jail. I am not sure about this one. How is it generally spelt in the Britain? While I spell it gaol, most people and media spell it jail.
Programme/program. As above. I spell it programme but mostly it is is not.