Ubuntu

You can find armhf Ubuntu images on their website. Up until release 13.10, Ubuntu had complete distributions packaged and available, but for the 14.04 release there is only Ubuntu Core packaged for armhf. Ubuntu Core is a minimal set of packages with which to get started, but you'll have to "roll your own" distribution if you want to do anything. Note that they have a full repository of packages compiled for armhf, it's just that a complete set of packages is not available in a single cd image

Both AllWinner and Ubuntu are members of Linaro, and Linaro has supported Ubuntu on ARM for the last few years.