First off, I'm going to talk about my top finds. Trust me, there are a lot out there and I didn't download them all, but I probably went through a good 15-20 apps. If you have an app that isn't listed that you like for whatever reason, post about it and I'll look into it! Make sure if you post an app below, that you give as much info as possible about it (and you've tried it on your nook)
Pros: Has a wide variety of books from major publishers, store sync's well with app, many options for viewing, allows you to import epub and pdf books.
Cons: Kinda basic, changing pages via the scroll bar doesn't work well, don't seem to be able to export books easily.
Bottom Line: Although it's a solid app, it doesn't have nearly as many books as the Kindle nor does it have as good a reading experience as other apps. With that said, it does offer some books that the Kindle store doesn't. I recommend this if you're loyal to B&N.
Pros: Nice interface, huge store with major publishers (more than the Nook), good viewing options, allows import of epub and pdf books.
Cons: The app redirects to a webpage for the store, which doesn't work as flawlessly as other apps, Like the NOOK app, changing pages via the scroll bar doesn't work well. The mobi format isn't that common and doesn't add for easy exporting.
Bottom Line: The Kindle app offers more choice in books than any other app, but the reading experience still lacks somewhat. It has just as much options as the Nook, but being able to customize it more would have been nice. It is very similar to the Nook in terms of usage. If you are loyal to Amazon, it's great.
Pros: Free books rented from local library, also offers audiobooks.
Cons: Selection varies depending on your area, Library account needed, there is a wait on most books, the app itself sends you to a webpage.
Bottom Line: This is a good complimentary app IF they offer anything for you in your area. Out of the three area's I have tried, only one had support for it. Free is always nice!
App: Laputa (free version)
Pros: Free books from both major publishers and independent writers, many Public Domain books, support for Chinese books, allows for easy import/export (due to epub and pdf file types), Multiple sources from which to get books from, Virtual shelf interface.
Cons: Reading experience lacks, most books are bootleg (therefor illegal), small buttons make it almost impossible to touch, many links in the stores are broken, misspelled/missing text within downloaded books.
Bottom Line: If you don't mind getting books illegally, it has a lot of major series (Lord of the Rings, Harry Potter, Sword of Truth series, Holmes, and many more). Most (if not all) of the downloaded books are in epub format so importing them into another reader is easy. Right now (apparently with the last app update), book covers is broken, so to utilize that feature in any reader, you have to manually download and add them. Not many reading options don't help the reader at all. Good way to get free books, but not to read them.
Pros: Best reading experience, many many options (from font size to margins), multiple library views, categories, and tags, Store works OK with a lot of public domain and creative common books, along with paid books, importing books is really easy, as is setting up cover art (if the book doesn't already come with it), Support for Catalogs and easy "Last Read" button, also support for Adobe DRM (which I have not tried out)
Cons: The paid section of the store doesn't offer as many books as Nook or Kindle, but still has a good amount, plain Home interface and store.
Bottom Line: Although the store lacks compared to a big company such as Amazon or B&N, you can find many books with this app. There is no reading experience as good as this one, with options to change text, brightness, orientation settings, day/night colors, margins, and even advanced formatting to override the books initial formatting to suit your style. The library offers both "bookshelf" view and "list" views, which can be sorted to your desire independently. List view also offers tabs to view by Author, tags, and Collections (some books come preset with tags, others don't. Either way you can add your own, and your own tag types) By far the best way to view epub and pdf books, I just wish they had support for mobi and other formats so that I could import my kindle and nook books that I have.
Each of these offer different reasons to use them, but if you can find your ebook in epub or pdf format, Aldiko gives you the best reading experience by far. The fact that it makes it so easy to import, download, and use ebooks is refreshing compared to the Kindle and Nook. Although I do not fully understand Adobe DRM, because Aldiko supports it, it seems to only enhance it. On a final note, I downloaded the first book from Harry Potter from Laputa and imported it into Aldiko and read the first 4 chapters. The file was OK, with some spacing, spelling, and formatting errors that I KNOW and official release of the Harry Potter book would NOT have.
I will be updating this with further information and maybe other apps when I can. Let me know what you think and if you have different experiences than me (or I got something wrong)
PLEASE NOTE: I'd like to say that I do not condone getting ebooks illegally, however one of the apps I talk about above (Laputa) does allow you to do so (at the cost of spelling errors, formatting errors, etc.). I also believe (not 100% sure, but it makes sense) that the law on ebooks would be similar to the law on video game ROM's, that is if I won the book I can technically download a free version of the ebook if I can find it, such as the case with the Harry Potter book I mention.