You can define your own OPDS book source (like a calibre managed collection on your desktop).
I keep trying others and coming back to this. It seems to work better than any of the others generally speaking, but it has foibles. The biggest one is that is apparently caches too much information somewhere and deleting a book won't get rid of it. You have to pretty much re-install from scratch when it gets confused enough. This will probably be a problem for me only while I am tweaking my books and changing them.
Sometimes going into the android app manager and force stopping and clearing the cache and removing /sdcard/Books/.FBReader helps, but not always.
The thing that is appealing is the controls for just about everything. Manipulating them may not be really elegant, but almost everything can be tweaked.
This can also read almost any format book, but I've pretty much decided I like epub enough that I want to convert all my books to epub, so that isn't a big factor anymore, but I do have a few mobi format books that don't seem to convert well.
The biggest problem with FB Reader is the same as kindle - no access to the separate table of contents (.ncx) file, it can only see any table of contents that happens to be built into the book text. In many books only one of the tables is very accurate, so it would be nice to have access to both of them.
Another annoying thing is that links on the page that happen to be near the edges can't really be clicked to follow the link because it interprets that as a page turn instead of a link click.
You can define an OPDS source in here as well.
No MOBI support.
The initial reader options are a bit strange (for instance disabling css by default). Even when you turn back on all the css options, it still doesn't render as well as FB Reader (for instance, the first word in the first paragraph of each chapter in Game of Thrones is bigger than the others. FB Reader shows that larger letter, Moon+Reader does not).
There is something called “Preview with publisher formatting”, but it loses the ability to reflow text for some reason.
On the other hand the smooth scrolling is very nice in Moon+Reader. You can do stuff like scroll the place you stopped to the top of the page before exiting - very convenient as a way to pick up where you left off. It sometimes seem like a more convenient way to read as well, simply scrolling up a bit to bring the rest of the current sentence into view.
I've decided the navigation in Moon+Reader is too annoying. It won't follow the play order in epubs when advancing from one file to the next, so you get weird things like turning pages from the cover going directly past the body of the book to the end. It also does something that perhaps makes sense to the designers, but never made sense to me with weird back arrows showing up on pages sometimes.
I could almost decide I like this better than FB Reader, but so far the annoying bits are less annoying in FB Reader than in Moon+Reader.
This can also define an OPDS source.
Unfortunately, it has many drawbacks, the biggest being that all the carefully manufactured transparent .png files for chapter decorations I fixed up in my copy of the Game of Thrones books do not show up at all in the ebook version - there is just space where the .png files go.
No MOBI support.
Didn't take long to decide to uninstall this one.
No way to configure your own OPDS catalogs. The credits for the program say it includes code from adobe, and since adobe can't even build a program to read their own PDF files as well as alternate 3rd party programs read PDF files, I don't trust Aldiko to work at all.