Q:

How can I find out which apps I have already downloaded on my iPhone?

When you attempt to download an app that costs money, you will not be charged if you already bought the app. After you press buy and enter your iTunes password, it will say "You have already purchased this item. To download it again for free, select OK."
The problem is that I deleted hundreds of apps from my phone, some of which were paid for. Later on I might find an app I like but notice that it costs money. It might be an app I had already paid for, or an app which I got when it was free.
How can I know if I tap the buy button if I will be charged for the app or not?
In other words, how can I know if I owned a previous version of an app before?

A:

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

Go to Store > View My Account
Login
Click on "Purchase History"

You should now see all the apps you have downloaded before.
Stolen from caliban's answer here.

A:

Update: The easiest way to do this is to open up the App Store on the iPad, and search for the app. If you see it say "INSTALL," rather than showing a price, it means that you have purchased the app before, and can download it again for free.

One way to do this is to archive all your iTunes receipt notifications in your email account. This way you can search your email account for the application's name and see if it exists in any of your receipts.
The downside to this is that if the application's name changed it won't find it since your receipt will contain the application's old name. You could try searching for the seller's name, but that might change as well.
Another way to do this is to look at your iTunes purchase history. While this will have the application's current name (unlike in email archiving), there is no easy way to search through it.
Another difference between the two methods is that the Purchase History will contain app updates you downloaded, while the receipt emails will not.
Update: It seems that as of May, I no longer get receipts for free items via email.

A:

Apps that you delete on your iPhone are still in your iTunes. You should see there wich Apps you already payed for.

