Is there a dataset with news articles and their headlines?
The most widely used ones in text summarization research is the DUC dataset. If you see a paper using dataset "DUC 2015" or "DUC 2016" that's from here. 

I have also personally used the Reuters arcihve. You just need to download each article with wget or something similar. See also here.

The CNN / DailyMail dataset is also widely used in summarization especially in recent years, although it labels itself as a Q&amp;A dataset.