Very limited.
Facebook recently tested out a downvote button. The feature is available to a small number of users, on certain posts, however.
https://twitter.com/TaylorLorenz/status/961720791858544641
According to Gizmodo, however, it isn’t what you’d think. The feature was less a dislike button, and more a way for Facebook to better understand the sorts of things you want to see. In a statement Facebook gave to them:
[W]e are not testing a dislike button. We are exploring a feature for people to give us feedback about comments on public page posts […] This is running for a small set of people in the U.S. only.
So, I wouldn’t begin panicking just yet. The test was not far flung, either, affecting roughly 5% of Android users at the maximum. But it may get rolled out in the future; who knows?