Pretty well all D-SLRs and hybrid cameras now have some kind of dust-removal system that shakes the sensor (or a filter in front of the sensor) to dislodge dust particles. But not all dust particles dislodge so easily, and not all sensor debris is dust, so there's a good chance you'll have to clean the sensor yourself at some point anyway.
'Dust' can be light, 'dry' particles that shake free easily, but pollen grains are sticky, tiny airborne fibres may have oily content and tiny atomised specks of sea spray will contain salt, and these aren't going to just shake loose.
So look out for cameras with dust-removal systems by all means, but whatever the makers might claim, they will only deal with certain sorts of dust. It's all down to luck and the kinds of environments you shoot in.
