For the android I like iChess by Asim Pereira as well as his Analyze This
Chess Apps

I have an iPad and love it. There are a lot of chess apps and a lot of chess books in the iBook store. Here are some .
Shredder
Shredder lite
Chess.com
Stockfish
Learn chess! ( Maurice Ashley rules, puzzles lessons, etc)
Chessimo ( chess lessons)
Tactics Trainer
BC Take (chess puzzles like Knights tour by Maurice Ashley)
Openings
Pure Chess (nice looking 3D chess)
SmartChess! (Interactive book with board and movable pieces)
E+Chess (Interactive book with board and movable pieces)
Forward Chess (Interactive book with board and movable pieces)
Chess Opener
ChessU
Chess
Mate in 123
Chess camp ( puzzles and tactics based on the books with the same name)
iChess (puzzles)
Dino Chess (great app for teaching chess to kids)

The only chess app I can recomend from experience is Chess Pro (three levels: Free, lite, and with coach). It is an excellent app!

I use Android, and I really like the chess.com app. my other two favorites are Shredder and Chess PGN Master Pro.

A list of Chess apps I use. I do have many more, but decided to only list the ones I regularly use:

There is a great list of apps in these lists! Are all of these apps available for both Apple and Andriod, or are some only available for one or the other? I'm trying to decide whether I will get an iPad or not and I feel like the availability of apps will be a deciding factor!

My favorite is also Chess PGN Master Pro. Not sure whether there's an iOS version.
It can even open CBH books if you have the (free) CBH to PGN app installed.
There's a free version so give it a try.
bluetrane, you might want to try it as well because as far as PGN viewers go I have yet to find anything better and I tried all the well-known ones.

scid on the go, and droidfish. Both are free and excellent.
Scid on the go : for having database in scid format, can be used both on computer and android device.
droid fish : additional feature in this one is you can add comments to the game.

Chess Studio (gambit ebooks).
However, it's okay to use offline once you've downloaded an ebook, right?

@fburton I would think yes. I have that app and it comes with a free samples (I haven't bought a book yet) and it works offline just like forward chess, smartchess!, e+chess, and chess viewer (Everyman ) apps do

My favorite is also Chess PGN Master Pro. Not sure whether there's an iOS version.
bluetrane, you might want to try it as well because as far as PGN viewers go I have yet to find anything better and I tried all the well-known ones.
It looks great, it is only available for android. But I might get an android tablet one day so thanks for the tip.
Hey everyone!
I am thinking of getting a tablet for chess studies (That discussion can be found here: http://www.chess.com/forum/view/chess-equipment/tablet-for-chess-study)
Anyways, I was wondering what chess apps people recomend, both free or not and ones for apple or android. If you could let me know that would be great!