…with most e-readers, you can hook them to your computer with the charging cable (take the plug end off) and transfer e-book files to it as if it were another external drive.
SOME e-book readers even have Wi-Fi transfer capabilities.
As long as the e-book file is in the correct format, you should be able to do this. That means you can purchase files direct from publishers/authors and are not limited simply to one-clicking from the store of the e-book reader manufacturer.
If you have a tablet-type e-book reader with Internet access, you might be able to direct-download to your device (depending on the software).
With my iPad, I have both the Nook and Kindle apps installed. Also, I can buy PDF or E-PUB files from third-parties or publishers, email them to myself, and then open them in the iBooks app with no trouble at all.
There is also a program called Calibre (free) that will allow you to convert files that aren’t DRM’d, and will also transfer files to your device for you.