In iTunes, you can delete them and send them to the Trash. They'll be gone permanently off your computer
However, you can't really delete purchases from the App Store. All you can do is hide your purchases.
[A little later]
Huh. I was going to write to tell you where to go in the App Store on the iPhone to hide your purchases. Turns out that, while I know how to do it on the iPad, I don't for the iPhone. Sorry
But, I'm pretty sure it can be done... Anyone else know (cause now I'm curious how).
Marilyn