I came across a brief article on Wired.com with some pictures of Mars. The article describes the deepest valley in the solar system: the Melas Chasma on Mars. At some 5.6 miles, it's quite a bit deeper than anything we see here on Earth.
The 3D rendered image they showed (high-res image linked here), showed some landforms that looked remarkably similar to unconfined, subaqueous debris flows that we can see here on earth. Basically, a turbidity current - which is a gravity-driven cloud of debris and fluid (some good videos of modeled versions here). One of the remarkable things about the Mars image is how clearly the leading "toe" of these debris flows stands out (arrows point to several of them - along with a nicely developed fault scarp and hummocky block of wasting cliffside).
I'm not sure how the mechanics of these things work on mars, but without a thick atmosphere to help "cushion" the flow and allow it to travel long distances, I wonder if it's Mars' reduced gravity that helps these things travel so far.