Laputa Ebook Reader

There are many ebook readers available, best known is probably Amazons Kindle but I prefer the Laputa reader. It is easy to handle and you don't have to set up any account or  give your credit card details as you have to with the Kindle app.
You can download plenty of books for free from different sources like Gutenberg and Avayewn. The books are stored in your library and you can also sort them into different collections. The collection of books is really amazing and I couldn't find any better free book reader on the market at all.

When you read you can choose if you want to have settings for day or night, you can stop your phone from going into standby, change the font size and even choose how you want the pages to turn to the next one

Aldiko

Aldiko is also a good ebook reader for android phones. It has access to different book shops where you can download books, beside the paid books you can also find a nice  selection of free books. The Aldiko reader has not as many features as the Laputa reader but it got one big advantage: It can import your pdf files which means also ebooks or any other files in pdf are readable and it also remembers where you stopped reading and let you jump straight to that point when you return.
As I have many ebooks in pdf format I usually use Aldiko to read them as I prefer it instead of the normal pdf reader which was pre installed on my phone.