Automatically, and freely, download PDFs for a set of references
The answer here uses proprietary/paid software. I propose a FOSS solution that works reliably for this task. 

The cross-platform software JabRef has integrated fulltext fetchers to download the fulltext for any entry in the library. Import your bib file into Jabref and select a number of entries. Then, from the Quality pull-down menu, select Lookup Fulltext documents. However, you still have to manually confirm the download in a pop-up. But this is still just a bunch of clicking 'OK's at the same spatial location (for each pop-up that appears sequentially) with the mouse. Jabref does the heavy-lifting in the back to correctly download the PDF and link it appropriately by matching it to each relevant citation entry.

The latest master build of Jabref is recommended, since there were some recent fixes to the IEEE Fetcher. https://builds.jabref.org/master/ (if IEEE matters to the OP)