Yes. Not all e-books, but most...
Some e-book platforms (Knovel, Springer, ScienceDirect, Wiley) provide e-book chapters in the form of PDF documents which can just be opened or saved in the same way as any other PDF document once you're logged in to the platform.
Some e-book platforms (Ebook Central, VLeBooks, DawsonEra, EBSCOhost) offer a download function that allows you to download the whole book for a number of days. The number of days you can download the e-book for will vary from platform to platform. You may need to register a separate username and password in order to add the e-book to your Bookshelf before you can download it.
For downloading whole e-books, you will need to open the e-book file (usually .acsm) in Adobe Digital Editions (ADE) to bypass the Digital Rights Management (DRM) of the file. Once you've done this, you can continue to view the e-book in ADE, or use an ADE-compatible app to view on your mobile device. You will need to register your Adobe login with the app in order to download the e-book, but once you've set that up, you won't have to open the e-book in ADE beforehand. Downloadable e-books can't be viewed on a Kindle (excluding Kindle Fire).
