Well, I do a combination of both. In a place like Thailand I gave my clothes for laundry... costed THB40 per kilo but saved me effort & time. Where it is expensive or I have to move places this option does not hold good. I am all for washing it myself.
Depends how light and how long someone travels I suppose, but that's another subject...
There are some laundrettes in Australia, and probably plenty around tourist areas.
I wash my clothes myself in the bath or shower, although jeans can take sometime to dry.
I was in Southern Greece a couple of years ago, camping with a few friends. I doubt it could have been hotter anywhere else in the world. We got up, did our washing, had breakfast (we used the little taverna across the road that gave us a good deal - as we were regulars) and by the time we finished about 1/2 an hour later all the washing was dry. It was just so incredibly hot. Long live drinks coolers.