While I do love my Amazon Kindle Paperwhite I still read quite a bit on my tablet. Whether it's a book, magazine, or online article, tablets are pretty much the ideal vehicles for reading all of this content on one device. What are the apps I use? Read on for some favorite picks for consuming this type of content on the iPad and Android tablets.
iPad
Books
iBooks: While I'm not crazy about the bookshelves in iBooks, I do like using this app to read books and PDFs that I've created on my Mac or iPad. The reading options are solid (I love the way definitions are displayed) and if I'm not reading a book in iBooks, I'm reading it in the Kindle app just for the cross-platform versatility. App is free, content costs vary.
Magazines
Newsstand: While the fact that I can't easily put the Newsstand app inside of a folder drives me batty (I know it's like its own folder), I will reluctantly admit that every magazine subscription I have, that I read on my iPad, is via this app (early Zinio use was crash filled and disappointing). Do I wish that it was combined with iBooks? Yes, but at the very least Newsstand keeps the magazines together in its own annoying little way and makes paying and managing subscriptions simple. App is free, subscription costs vary by publication
Online Articles/ Blogs
Pocket: To be perfectly honest I use Pocket on every single piece of technology I own that it's available for. I throw articles into Pocket several times a day and find it's my ideal way to consume long form pieces published online. Also available for Android. Free
Android
Books
Kindle: While syncing is not as seamless across devices as it is in the iBooks universe, it's still far better than it is with the Nook app. Kindle has a huge repository of books and is available on almost everything (including Windows 8). I love being able to have the same book on the Paperwhite as I do on the Samsung Galaxy Note II and so this is where I buy and read the vast majority of my books even though I dislike the way the apps looks and works in landscape. App is free, content costs vary.
Magazines
Zinio: The clear king when it comes magazine reading on both Android tablets and the iPad. Not terribly enthused about the design (I find the dark background tricky to read and navigate) but it gets the job done, looks great on the Nexus 7, and I have yet to discover an equivalent magazine app that works better. App is free, subscription costs vary by publication
Online Articles/ Blogs
Press: If you're a fan of using Google Reader to catch up on all the blogs you read then this is the app for you. It's clean (not as visually distracting as Flipboard) and is a delight to use on the Nexus 7. Now if this app were only available for the iPad, my life would be complete. $1.99
(Top Image: Joelle Alcaidinho, all others as linked above)

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For Android, my preferred reader is actually Aldiko. I've had it since the G1 days and it just works. Add the Aldiko sync app and it can automatically sync your books between multiple devices as well. I also like that it handles epubs, so reading books from OverDrive is simple.
Why Pocket and not Instapaper?
I clicked on this hoping for some interesting recommendations but I don't find it helpful in the slightest. For example: Pocket is "my ideal way to consume long form pieces published online." Umm, care to tell us why? Likewise, the author doesn't like the way the Kindle app works or looks, but notes that it allows users to have the same books on different tablets. Are there any reasons for those of who aren't gadget-bloggers and own only one tablet to use it, then?
I read my magazines on Next Issue. It has more than 50 monthly magazines and a flat rate of $9.99 a month. I'm saving money!
Yeah, I'd like more discussion of what makes an app a favorite. I personally use the Kindle app on all my devices, and I love it. I especially like the font/background color options, allowing me to read white (or is it pale gray?) text on a black background, which is much easier on my eyes on a backlit screen.
I prefer the Kobo app for reading books and magazines. Free app and you can d/l content on any device. You aren't limited to one device like Kindle.
I like RockMelt for iPad & iPhone (& it's free!). It pulls all of the sites I regularly read into one browser, organizes them, and shares with me what my friends are reading: http://www.rockmelt.com/
I use the Kindle app, mostly, with Feeddler Pro for my Google Reader feeds, and the occasional Newsstand magazine and the NYTimes. I often send lengthier articles to my Kindle email address.
My favorite feed reader is Flipboard on a Samsumg S3. The size & resolution of the screen make it quite pleasant to stay on top of articles. Other than that, Google's book reader is my go-to.
All my physical and e-books are all purchased from Barnes and Noble and their Nook Store. Why? They have the largest library, I prefer to give my book business to a dedicated book seller and especially because I never wish to see what happened to Borders happen to Barnes and Noble. I read all my Nook books on my iPad.
You aren't limited to one device when you buy from the Kindle store either. I have the Kindle app on my iOS, Android, and Windows devices.
I also love the Kindle app, the only thing I dislike about it really is the landscape view.
The only thing I dislike about the Kindle apps as stated above is the landscape view which I find really difficult to read. I think the Kindle apps and ecosystem are a great way to read books which is why I have this app on every device I own and chose them for my standalone eReader. As things get more tied to ecosystems and less portable I think that being able to have something that's not tied to an Apple product or an Android or a Windows product is huge.
While I'd love to go into all of the reasons why I love certain apps these weekly roundups aren't the forum for it, we shoot for brevity. We go into the pros and cons, likes, dislikes of apps when we do standalone reviews...perhaps there should be one for Pocket?
Originally started using it because I liked the way it looked and it was free whereas Instapaper was $4. Now that I've been using it for awhile now and so have a laundry list of reading materials and so switching to something else is not appealing especially when I'm happy with Pocket.