In Europe, a person holds the rights for publishing a picture of himselve... "If not being of public interests".
This is a very unclear formulation and sometimes goes for "lookalikes", too. Especially if it goes with a sexual or otherwise unpleasant context. This is a civil law case and needs the complainant to take action for an injunction.
But anyways, like Jiraiya said, this holds true mainly for the creator, but also for a publisher. Under some circumstances, a "publisher" even can be someone who shares a download, or the downloading website. I bet it is somewhat similar in other countries. Therefore most of the lookalike creators are somewhat discrete.
Because it is a civil law thing and no criminal act, only downloading and keeping those looks isn't illegal.
It is an other pair of shoes in very restrictive countries, where some sorts of porn, or picturing a religious or political person are forbidden... but I think you know if you are living in such a country or not.