Actually delete an application directly from your iPhone is very simple and easy. Instead of forcing you to connect it to your computer, load iTunes, and remove your apps that way. Apple actually made it so that you can remove them no matter where you are and your can sync back to iTunes later.

Just touch and hold an icon (select it which one app do you like to touch on your iPhone "Home Screen") for a few seconds (1-2 seconds) will make your icons ‘wiggle’. For each application and game installed from the App Store(you can’t delete the stock apps) you can see a small "X".

Tap the small "X" at the left top of your icon and you are asked if you want to delete that specific app or not. For example i just tap the small "X" on Hero of Sparta icon. If you tap delete it will actually delete the application and remove the icon without you having to connect your iPhone or iPod Touch to iTunes.