So if you're looking for online chess, the chess.com app is the best. If you're looking for pure chess strength, Stockfish is your choice. If you want to expose a bit more about the engine, Hiarcs should be your first preference. If you're looking for amazing integration, SmallChess is a good candidate. If you just want some causal games and easy puzzles, Shredder is your choice.
Best iPhone Chess Apps?

I have Hiarcs, Shredder, and Stockfish on the iPad. I use Hiarcs the most for analysis because it contains the Hiarcs opening book, and setting up a position (middle game and endgame) is quicker and easier. The Hiarcs opening book offers more data than Stockfish's opening book.
I have gone through all 1000 puzzles in the Shredder app twice, and am working my way through for the third time. The puzzles are the best part of the app.
Stockfish may be stronger and is free. Playing against a handicapped engine, I find that Hiarcs is best for imitating human play. Unless you are a top GM, the strongest engine may not be your most useful tool.
There may be differences in functionality between the iPad and iPhone.

Fritz, on the iOS is a good example of how a good engine can screw up. The engine is noticably weaker than its PC version. In fact, it's weaker than everything listed here. It's slow, doggy and no retina support. Hasn't been updated for years, there is nothing good about the app.

If you're looking to just play a game with a random human opponent or a friend, try Tall Chess (tallchess.com). It's free, and frankly, the most well-designed iOS chess app out there (in my opinion).
Disclaimer: I am the lead iOS developer on this project.
I've tried Tallchess. It's doesn't work. Unable to find anyone to play with and the interface is crap. A chess app that you can't use to play a game.
The app has a dozen of five star reviews. They are obviously fake - all written by the developers themself. All wrote pretty much the same thing, all five stars and all wrote the reviews on the same date that the app was released.
I've written an email reporting the incident to Apple. Manipulating your own app with fake reviews violates the AppStore developer license and Apple will surely ban you.

Yikes! What a welcome to the Chess.com community. MBrades, I'm sorry you don't like the app, but I'm not sure such a mean-spirited response was warranted. If you don't like the app, simply don't play! The parent asked for an iPhone app to play chess with other humans, and I offered one option, with a clear disclaimer.
As to your charges of fake reviews and manipulation: since "the developers" consist of myself and only four other folks, we certainly did not "write them ourselves" (and there are 34 5-star reviews as of today, not 12). For dozens of real testimonials by real people, just take a look at what folks are saying on the web:
https://twitter.com/tallchess/favorites
http://uncrate.com/stuff/tall-chess/
I created a Chess.com account to reply to this post, but I can't say that this experience has encouraged me to come back again.

Apps for FICS there is online chess , live chess, and playchess.com. I suggest you go the app store and type FICS under the search.

I use Chess-Wise Pro to connect to FICS. It also has 300 tactics problems and many other nice features.

timothyarnold, about TallChess:
Maybe you could answer some of my questions. Your response might also help promoting your app.
Q1: Will you and your team add local playing support?
Q2: What's the main motivation for having a rectangular chess board? A chess board has long been a perfect square. Why you and your team want to try something new?
Q3: I've having a little problem finding a random opponent. What do you think?

There is absolutely no doubt that the best chess app on the store... is MY APP.
101 Chess Checkmate Puzzles. Search: 101 Chess (It is 19th when you search just chess... which is pretty good for a new app) Anyway....
Download it. it is free. All the white pieces are 'clickable' and it is doing very well. if you have any suggestions or would like to suggest some puzzles I can add them!!

There is absolutely no doubt that the best chess app on the store... is MY APP.
101 Chess Checkmate Puzzles. Search: 101 Chess (It is 19th when you search just chess... which is pretty good for a new app) Anyway....
Download it. it is free. All the white pieces are 'clickable' and it is doing very well. if you have any suggestions or would like to suggest some puzzles I can add them!!
101 puzzles is less than a week of training.
I already have apps with 1200 problems (Chess Quest), and tens of thousands (Chessimo and Tactic Trainer). See http://chessskill.blogspot.com/2013/02/chess-tactics-training-on-ipad.html.

kinderchocolate. I was only being facetious. Honestly, what do you think.....
Any suggestions would be great. It's actually doing really well. I am very happy.
1. Chess.com's app, which I use to play live 30/0 games and then email PGN to myself
2. CHESSPRO app (from chess tiger), which I use to import that PGN and analyze the game with a strong computer
3. Shredder app, which I exclusive use for solving tactical puzzles as quickly as possible in preparation for my next live game on the chess.com app.
If you are willing to pay a monthly fee you could probably just use No. 1...
Chess.com is simply the best correspondence chess app. No question about it.