If you like to manage your eBook library and use it across multiple devices, download and install Calibre on your PC or Mac.
Calibre is an app that can search for missing metadata/book covers, convert between different non-DRM formats (MOBI, EPUP, AZW, etc,) and sync with a wide range of devices (Android, Kindle, iTunes to name a few popular ones).
The Android market has a wide spectrum of eBook/Comic readers that all have inherit features and limitations. One requirement I have for any eBooks reader is the ability to side-load media- that is the ability to add eBooks from another market/source outside of the associated eBook market (Amazon, Barnes & Noble, etc). Some apps allow this readily but some make this task difficult/impossible as they want to tie you into purchasing only from their market.
A few readers that I find myself using on Android are:
Moon+ Reader
This is currently my favorite as it allows browsing the SD card for eBooks (i.e. no need to import or put in a specific folder), it supports EPUB, MOBI, CHM and HTML eBook formats (plus others) as well as CBR & CBZ Comic Book formats.
The free version has advertisements. The $5 pro version removes the ads and adds PDF support, text-to-speech and other tweaks.
Aldiko Book Reader
This is a no-frills eBook reader that supports EPUB and PDF files. It is fairly user friendly save for eBooks need to be imported into the Aldiko library into /sdcard/ebooks. The importing makes a copy of the original file and may end up with duplicates (i.e. in both /Books and /eBooks).
A premium version costs $2.99 and removes ads, adds the ability to add nodes and highlights and receives updates before the free version. Additional free and paid plugins allow for eBook sync via Dropbox.
Kindle
This connects to Amazon’s market to download any books purchased from Amazon. Sadly, the Amazon app does not allow direct importing of 3rd party EPUB/MOBI files. It does creates a /sdcard/kindle folder where you can drop converted AZW/AZW2/AZW3(/MOBI?) format eBooks (converted by Calibre) that will also be added to your library.
Note: if you are on a PC and running Android v3 (ICS) or later, the /kindle folder is not presented over the MTP (Media Transfer Protocol) USB connection. Earlier versions of android support MSC (Mass Storage Controller) USB settings and will let you directly access the folder. If you are on ICS or later, you can use an Android file explorer such as Astro to move files from the /sdcard/Book folder to the /sdcard/kindle folder.
If you are using a Mac OS system, you will need the Android File Transfer utility to access an ICS or newer device.
Nook
The Nook reader is the Barnes & Noble storefront ebook solution. It also allows for reading of EPUB books added to the /sdcard/Nook folder.
Kobo
Kobo reader ties into the Kobo store (go figure!) and allows for importing of EPUB books from the SD card. As of yet, I have not figured out exactly where it stores the books it imports…
Google Play Books
This is the most useless of all the eBook readers. It is included by default on all newer tablets and it allows you to read any books purchased from the Google Play store. i.e. if you have an EPUB/MOBI/PDF that you want to access, you need to use another program.
There are a plethora of other readers but these are the ones that I have tried and sometimes still use. :)