When a dataset is available online, it doesn’t mean anyone may share or reuse it without conditions. Check the terms of use or the licence. Creative commons licences are widely used. The most open Creative Common licence is CC0 (CC zero), but the author is free to put restrictions on sharing and reusing the dataset: they are ordered here from the most free to the least free licence.
Source: Wikimedia Commons.This picture is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
On Harvard Dataverse, the dataset "Replication data: From Baghdad to London" is licensed CC0 (under the tab Terms).
