Yes you can! it may take a bit of fiddling but although I would love to resist Amazon's world domination project, I find Amazon format books are both cheaper and also better formatted for reading.
Apprentice Alf is the leader in this dark art, in his blog, http://apprenticealf.wordpress.com/ (see his comment on this post, below). You will find useful discussion and links to the up to date conversion tools there.
The current tools are here: http://www.datafilehost.com/download-a28d695b.html: download and unzip the folder. Don't be daunted by the technical chat, just follow the instructions in the ReadMe files.
To free up Amazon e-books (this is on a Mac, there are similar facilites for a Windows pc) - move the zip file DeDRM_5.0.app.zip onto your desktop (or other convenient folder), click it to unpack to a curly icon DeDRM 5.0.app.
Your Kindle book files are in My Kindle Content. They don't have helpful titles, but sort them by date, and it's the .azw file that is the book. Drag this onto the curly icon and it will save a freed up copy of the book for you. You should be able to upload that to your reader, via the free Calibre software or even via your normal reader software.
Calibre is very handy, search to download it for free (be fair, do donate). Once Calibre is installed, you can install the DeDRM plugins:
Open Calibre preferences > Plugins > button at the bottom, Install plugin from file > Navigate to the DeDRM folder with the Calibre plugins > click on one to install it
Repeat until all are installed. Restart Calibre.
Then, you can just add the book file to the Calibre library and upload it to your device - select Autoconvert and it will do the conversion as part of the process.