Most of the time I don't, but sometimes I'll say something that sounds really Australian, like if I say 'how ya goin'. But Western Australian's have a more neutral accent than those over East (they'll be more like Steve Irwin). I notice it more if I'm talking to people with another accent, but most of the time it's only if someone else makes a comment that I'll be aware of it.

Also I lived in London for 9 months and my family reckoned that my accent sounded more 'English' towards the end of that, but I'm pretty sure that doesn't happen over 9 months.. I really do love English accents though so maybe I'm just prone to picking them up more quickly :P