Droidfish (
Free) : A chess program for Android devices developed by Peter Österlund, author of Texel (formerly CuckooChess). The main engine for the program is Stockfish (authored by Marco Costalba, Joona Kiiski, and Tord Romstad).
Some of the features of Droidfish include
The ability to use polyglot books and CTG books in addition to the internal book
Support for Gaviota tablebases
Importing additional UCI engines
Play against an engine, or another player, or analysis mode
Adjustable playing strength
Edit board
Scid DB support using "Scid on the go"
PGN import/export/edit
Here are some screenshots: