The US format is indeed awful but so is the European one really. ISO-8601 is the only one that makes sense, although the concept of months isn't really useful at all. But it's not always unambiguous. ISO-8601 supports local time. It's only an unambiguous timestamp of the time zone is included.
There are many different European formats, some countries even use (a slightly modified version of) ISO-8601, ex. in the Nordics.