Will Salesforce ever drop support for Classic

The Lightning Experience FAQ (last updated October 2016) includes:

Q: Can I still use Salesforce Classic?
A: You have the choice of when you want to move to the new Lightning Experience UI and which users you want to migrate. You can continue to use Salesforce Classic as long as you like, and we will continue to support the Classic UI.

Salesforce has no plans to drop support for classic. It will be around for a long time to come. You'll notice that PDFs are still rendered in classic, that lightning components can be used in classic and that visual force pages can be used in a lightning container in lightning pages. There are far too many orgs that have a lot of money invested in custom visualforce pages for Salesforce to consider forcing them to lightning.

Salesforce.com has not announced any plans to remove Classic at this time. I would expect that salesforce.com is trying to get rid of Classic as soon as possible, but they will not be able to do so until they can convince 100% (or very close) of their major clients to move to LEX entirely. This means that they need to have 100% feature parity with Classic, and offer enough features that are LEX-only to entice large clients to move to Lightning despite the costs of doing so. Based on what I know about how larger clients operate, I would expect that the absolutely earliest this might happen is 2020, with a more realistic outlook between 2023 and 2025.