Yup, you read it right!  You can play tons of the great NES classics on your iPhone.  I'm linking directly to the Google Code page since this is the most all-encompassing place to find directions and info/downloads for the iPhone.

Link here or press the 'Play' button. 

Neverball is available through the iTunes App Store and is a great game.  Your goal is to roll yourself (a ball) through various levels and collect as many coins as possible.  The game is similar to Super Monkey Ball but appears to be free.

To roll your ball you utilize accelerometer and actually move the iPhone.  It takes a little while to get used to it but after 15-20 minutes you should be passing levels and having fun.

This is truly one of the better games that's been created for the iPhone/iTouch in a while.  Nine Men's Morris is a very old game that was created during the Roman Empire.  In it, you play against real people to overtake their pieces in a multiplayer environment.  When you go to the site you can actually see how many people are online at any given time which is very cool. 

I'd never played this game and got whooped in about 2 seconds.  But after playing for a while I did get better.  Be sure and read the instructions!! 

The wikipedia page about the game says:

Each player has nine pieces, or "men", which move among the board's twenty-four intersections. As in checkers, the object of the game is to leave the opposing player with no pieces or no legal moves.

Placing the pieces

The game begins with an empty board. Players take turns placing their pieces on empty intersections. If a player is able to form a row of three pieces along one of the board's lines, he has a "mill" and may remove one of his opponent's pieces from the board; removed pieces may not be placed again. Players must remove any other pieces first before removing a piece from a formed mill. Once all eighteen pieces have been placed, players take turns moving.

Moving the pieces

To move, a player slides one of his pieces along a board line to an empty adjacent intersection. If he cannot do so, he has lost the game.

As in the placement stage, a player who aligns three of his pieces on a board line has a mill and may remove one of his opponent's pieces, avoiding the removal of pieces in mills if at all possible.

Any player reduced to two pieces is unable to remove any more opposing pieces and thus loses the game. 

Flying

In one common variation, once a player is reduced to three pieces, his pieces may "fly", "hop" or "jump" to any empty intersections, not only adjacent ones. Some sources of the rules say this is the way the game is played, some treat it as a variation, and some don't mention it at all. A '19th Century Games Manual' calls this the "truly rustic mode of playing the game".

Sarkscape Games has created a sequel to the fantastic original Ninja Ropes.  This is one of the better games created that fully integrates all the functionality of the iPhone.  The game instructions say:

Ninja Ropes Extreme is a sequel to the famous Ninja Ropes game. Now you will fight against gravitational anomalies.

New gameplay, new challenges and new gaming experience. Show your best in the ninjas' secret knowledge and be first in the online top 15.

This is a must play.