The Moveslink software that manages to download stuff from your watch and uploads it to Movescount also keeps a backup of the files on your computer. Unfortunately this is some
xml file which is not necessarily directly compatible to other platforms. But there's help! Some nice guy wrote ambit2gpx, a tool that converts the Suunto style
xml file to a
gpx file that should be readable by most online services or training software suites.
If you convert the files with that tool you should be able to upload them to Runkeeper as well, even without having to upload them to Movescount before (if you don't like to do that for some reason), as Moveslink will store the files from your watch locally even if it cannot upload them to Movescount for whatever reason.
But unfortunately there does not seem to be some easy and automated way to do this yet.