Reading ebooks is the number one use for my Android tablets and I've tried quite a few readers over the past two years. Aldiko was my reader of choice originally, but it has fallen so far behind that I haven't even bothered to install it on the tablet I now use most often for reading (Nexus 10).
The readers I use today are:
1) Mantano Reader Premium
($6.99 - there is free Lite version and an intermediate Essential version for $2.99). My favorite in most situations for both epub and pdf. By far the best document navigation and library management if you have an extensive library (as I do). They have a paid cloud service for synchronization which I tried and quickly dumped. Rendering is not quite as good as Nook, but it allows you to install many TTF fonts. Reasonably good support with a user forum and an actual manual
2) Moon+ Reader Pro
($4.99, on sale through August 2013 for $2.49, the free version is much less capable). Extremely flexible with many customization options, and very robust - it can handle malformed epubs that other readers choke on. Also does CHM well. The interface is rather quirky and can take some getting used to: It breaks epubs by chapters and allows you to scroll smoothly within them, so it is my first choice for reading on a phone (one-handed), however that design also makes it hard to find your place within a large book. Can synchronize using Dropbox.
from Barnes & Noble. Although meant to work with the B&N Nook store, this is an excellent free epub reader that allows side loading and can be used with any non-DRM epub file. Not as flexible as the two mentioned above, it has the best on-screen rendering of any Android reader and pretty good within book navigation.
All three of these support Adobe DRM, but I always convert purchased ebooks to DRM-free epub before loading them on my devices, so I have never tested this. I buy books from both Amazon and B&N, and other vendors too (e.g., O'Reilly), but while I do use the Nook reader on my devices, I hardly ever use the dreadful Kindle for Android app.