I have a Kobo Glo with lots of legitimately purchased ebooks from Amazon and BN on it.
All it takes is the Calibre open source library manager and a couple third-party DRM-stripping plugins. Rarely, converting from AZW, you'll need a bit of CSS skill and a text editor to track down a conversion glitch.
Of course this entails an account at each vendor to buy the books. Downloading is handled by the Amazon and/or Adobe Digital Editions (BN/Kobo) apps used by those accounts. Just don't let the apps fondle your ereader -- that's what Calibre is for.
This technique probably works for Nooks as they're epub-native like Kobo. Not sure how easy or effective converting into AZW/Mobi/etc would be for Kindlers, but these same tools might well do it.