Unfortunately, the choice of ereader is also your choice of bookstore.  If you buy a Kindle, you're shopping with Amazon; if you buy a Nook, your store is Barnes & Noble.  You can either buy a more expensive multiformat option, like an iPad, or you can suck it up and make a difficult choice.

I chose the Nook, because it supports the defacto standard ebook format, epub, and I'm just a standards kind of guy.  Practically every other ereader and ebookstore also uses the epub format (with Amazon being the notable exception).  Unfortunately, the epub format allows distributors to use any form of DRM they like.  Fortunately, it's not hard to crack.  The go-to site for ebook decryption is i♥cabbages.

Borders/Kobobooks/Adobe Digital Editions
Borders' ebooks are provided by Kobobooks.  Most titles are offered in multiple formats including web-based, pdf, and epub.  The epub titles (and the pdfs) are encrypted using Adobe's Adept algorithm.

Enter ineptkey and ineptepub.  The former will retrieve your validation key (generated by Adobe Digital Editions), and the second will use that key to decrypt your ebook.  Just enter your input file, your output file and press "Decrypt".  You're done!

Barnes & Noble
B&N uses a variation on Adobe's DRM format, so the process is similar.  Use ignoblekeygen to generate your decryption key by entering your B&N.com login name and the credit card number you used to purchase your ebook (this number is used ONLY to generate your decryption key; it is not stored or transmitted).  Then use ineptepub to decrypt your book.

Amazon
Amazon opted to use the proprietary azw format for their ebooks, which is itself a variation of the mobi format.  These titles can be decrypted by unswindle.  This script will launch the Kindle Reader, where you will choose the title to decrypt.  Once the title opens, close the reader.  The script will read the key from memory and open a file dialog where you may specify where to save your decrypted file.  Kindle books can also be decrypted using the command-line tool skindle.

You may also occasionally see Amazon files with the tpz (Topaz) extension.  These files can also be decrypted with skindle, though conversion is more involved.  A Google search is helpful here.

iBooks
iBooks titles also use the epub format, but they can not yet be decrypted.  The titles use the same "FairPlay" encryption scheme used by iTunes' music and video downloads, however, so it's surely just a matter of time (audio and video can currently be decrypted with "Requiem"; search your favorite torrent site).

Once decrypted, your ebooks can be converted as necessary by a program like calibre.

The culprit, of course, is Digital Rights Management. DRM is a way of tying digital content to the original purchaser. Usually, this also means tying it to a specific hardware and/or software device. Content producers say this is necessary to prevent piracy. They're wrong.

While DRM may be adequate for stopping casual sharing (such as when I "give" my friend the new Snoop Dogg album I just got off iTunes), it does nothing to deter the dedicated pirate, who simply gets his media from illicit, DRM-free channels (such as torrents, newsgroups, and direct-download, like Rapidshare and Hotfile. Or so I've heard). The loser, of course, is the consumer, because these technologies, like their analogue in the hardware world (I'm looking at you, Apple!), prevent consumers from using their legally purchased products in the way they want. Want to listen to that iTunes album on your Android phone? Sorry, Apple only. Want to read that Amazon ebook on your Barnes and Noble Nook? Nope. How about that iTunes video on your Linux box? Sucks to be you.

The irony is, you are perfectly within your Fair Use rights to change formats or otherwise use your legally purchased content in any way you see fit for your personal use; however, circumventing DRM in order to exercise those rights is a violation of the Digital Millenium Copyright Act. Which is paramount? Ask your lawyer. Then ask another one. You'll likely get two different answers.

Unless, that is, you live in the Fifth Circuit. There, Judge Emilio Garza recently made the commonsense ruling that merely circumventing DRM is not illegal, provided the underlying reason for doing so is non-infringing (I'm parapharasing). In other words, if it falls within your Fair Use rights, you can break DRM to do it.

This is great news...if you happen to live in Louisiana, Mississippi, or Texas. For the rest of us, it technically has no legal bearing; however, it does establish precedent that may influence similar cases in other jurisdictions. Ultimately, this issue will have to be decided by the Supreme Court, or Congress, or even by the Library of Congress (which has the power to grant DMCA exceptions).