I am a beginner to eBooks, and as somebody who has been "outside" of eBooks I've only ever heard of Amazon's Kindle and seen a variety of options for purchase on Google Play.
I have recently purchased an Android tablet and I want to buy some eBooks, I know from experience with downloading music that different stores will have their own differing, and often, incompatible digital rights management systems.
What kinds of DRM are used in eBooks? Is it possible to purchase DRM free eBooks?
According to Wikipedia, there are four main ebook DRM schemes in common use today, one each from Amazon, Adobe, Apple, and the Marlin Trust Management Organization (MTMO).
Amazon's DRM is an adaption of the original Mobipocket encryption, and is applied to Amazon's Mobipocket, KF8 and Topaz format ebooks.
Adobe's Adept DRM is applied to ePubs and PDFs, and can be read by several third-party ebook readers, as well as Adobe Digital Editions software. Barnes & Noble uses a DRM technology provided by Adobe, and is applied to ePubs and the older Palm format ebooks.
Apple's Fairplay DRM is applied to ePubs, and can currently only be read by Apple's iBooks app on iOS devices.
The Marlin DRM was developed and is maintained in an open industry group known as the Marlin Developer Community (MDC) and is licensed by MTMO. (Marlin was founded by five companies, Intertrust, Panasonic, Philips, Samsung and Sony.) The Kno online textbook publisher uses Marlin to protect ebooks it sells in the ePub format. These books can be read on the Kno App for iOS and Android tablets.
To answer your second question. Yes, you can purchase DRM free ebooks (Wikipedia lists a few places here.). Whether or not a book is DRM free will depend on the publisher/seller. It is also possible to remove DRM from some books, as there is opposition to DRM.
Some of the more enlightened publishers, including O'Reilly and Pragmatic Programmers, publish their technical books without DRM and in the major formats including PDF, .mobi (for Kindles) and EPUB. I expect other publishers will do likewise. Others watermark their books e.g. where the footer might say 'for Julian Harty' where the books are not DRM'd either.
Some of the "big" resellers, such as Amazon or Kobo, sell without DRM if the author/publisher requests it, but not generally. Furthermore, there are many non-book formats (e.g. Lightspeed Magazine) and independent, often crowdfunded projects (e.g. on Kickstarter).
Note that many DRM-free ebooks use watermarking, that is the files will contain information about the buyer. Since such data can be traced back to the leak in case of an ebook being illegaly shared, such measures detract from piracy but don't actively prevent it.