From what I've read on various websites:
- Hiarcs
- Shredder
- Chess pro with coach
- tChess pro
- Stockfish: free (open source), but a very strong engine
All these are very strong and will defeat any average player easily. Of course you can set the strength to your liking.
Chess pro with coach and tChess pro are universal binaries for iPhone and iPad.
You have to buy separate copies of Hiarcs and Shredder if you want to play chess on iPad and iPhone.
tChess pro has no landscape mode
My advice would be: get Stockfish if you just want to play chess. It is free, but very good, much better than other free and paid apps. Then if you want more specific features, purchase one (or more) of the other apps.
If you want to play remote with others:
- Social chess
- Chess - play and learn