You're a rat in a maze on the ultimate quest to find the cheese on various levels.  You click around the map only viewing a few tiles (3x3) at a time so you can't see the whole maze.  The maps start out relatively easy but as you get into the third maze and beyond they get rather tricky.

I liked this game and will probably play it a few times over just to see how far I can get.  If you like maze-style games you'll love this one. 

Let It Roll is a multiplayer game where you roll 5 dice and keep score.

The phone will save your game so even if you quit or turn the phone off it'll remember where you left off.  The Kudit site says:

Yahtzee-like dice game that can be played with any number of people. Works in portrait and landscape modes!

Lexitron is a great word based game in which you make as many different words as possible using the six letters provided.  I absolutely love games like this and Lexitron is no exception.  The main site's info says:

Lexitron is a fast-paced word game built around anagrams. The object of the game is to find as many words as you can in the time limit, but be careful-- if you fail to find at least one word that uses all six letters, the game is over and you can't move on to the next round.

 If you want to play Lexitron you'll need to get the Installer.app on your iPhone/iTouch which requires jailbreaking it.  I don't condone this act and be careful! :)

Your objective is to turn all the lights off but, it's not that simple because turning one off can turn another one on! Lights off is a mindbender and really fun.

The PowApps instructions say:

Just Tap on one light and you will switch it on or off, along with the four adjacent lights. You win after getting all of the lights to shut off.

Arrange the balls of the same color in straight lines of 5 or more. You can move the balls around and longer lines get more points. It's a little tricky at first but this is a great game.  It runs great and is definitely one of the better games made for the iPhone.  The info and instructions say:

To move a ball, click on it with the mouse (circle will appear) to select it, then click on a free cell in a field. To deselect a ball just click on another. If movement is possible, ball will go to the specified empty field. After each turn, 3 new balls are placed on a field (random colours & positions). Preview panel shows colours of the next 3 balls. You can alway force the next turn without moving anything. Click on preview panel. If the game field is full, game is over. Refresh page to start a new game.

Game goal is to arrange balls of the same colour in a straight lines (every direction). 5 or more balls on a straight line are removed and points are given. Longer lines give more points to you. Crossing lines count together.

You do not have to stay online during the game. You can disconnect from internet after complete page loading and play entirely offline.

Logic3 requires you to think, and think hard. Your objective is to get all the buttons to say 0.

There are a bunch of difficulty levels so I'd recommend starting out on 'Real Easy' or something like that. 

Lotto Web App is an application you can use to check lottery results all throughout the US. 

If you play the lottery you'll want to bookmark this.  The app runs smooth and has a simple design and layout.

DS Effects has created a fairly good version of Snood for the iPhone.  You want to aim and shoot the heats while matching up the colors in groups of 3 or more.  It's not perfect and I really want the real Snood on my iPhone but this will work for now.

Instructions:

Right and left arrows aim while the center button will shoot. 

Lumina Memory Game is an extremely high quality Simon style game for your iPhone.  CrossComm has created this game with audio and that really helps to keep track when you get more advanced.

It runs smooth and looks great.  Definitely play this one.

38i has created a remake of the old school game Lunar Lander in which you need to make the spaceship land softly on a planet.  To do this you're equipped with thrusters to counteract the speed at which the ship is falling.  The site's instructions say:

To accomplish a perfect landing, you have to touch the ground with a speed greater than -10m/s (not that you are descending, thus it is negative speed).
Tap on the thrust control to set the thrust engines to control you descent.

I have to say this is a really hard game.  I kept crashing the lander over and over and over.