If I buy an iPhone app will I have to re-purchase the app if I get a new iPhone?

I upgraded from the 3G to the iPhone 4 and forgot to backup and transfer my apps. If I attempt to purchase apps that I have previously purchased, will the Apple store charge me? Or will it recognize that I have already purchased the app based on my apple ID?

No, you will not be charged. You can re-download them in iTunes or directly on the phone. You'll have to hit the "buy" button, but after it starts downloading, you should see a message saying you already bought it once. The alert box includes a button to go ahead and re-download the app, which you will then not be charged for.

according to the caliban answer on SU:

To re-download all your apps into iTunes.

   1. First you need to authorize your iTunes. (Store > Authorize Computer)
   2. Next, check for available downloads (Store > Check For Available Downloads)

iTunes will then check for what you have purchased before, and give you an option to re-download your purchased apps.

To see a listing of all the apps you have purchased or downloaded, do this :

   1. Go to Store > View My Account
   2. Login
   3. Click on "Purchase History"

You should now see all the apps you have downloaded before