iTunes – Get List of Installed Apps

In addition to keeping your email receipts, you can also view your entire purchase history by viewing your account in iTunes. If you're signed in, click your account name in the top right, and choose the "View Account" option. On the following screen, the third section down shows "Purchase History", with a link on the right to see all your orders. You can see each order, listed chronologically, and jump to specific months and get more detail about a specific order.

I am not sure that is what you want but here is what I've done.

I keep my apps sync'ed and let iTunes download everything on my Mac.

However, as I do not want my main HDD to be filled by these apps, I moved them to an external backup drive.

To do this, I go to the 'Apps' section of my 'Bibliothèque' (I have a french version of iTunes, but you can find it in the listbox that is in the upper left corner of iTunes main window).

There, I choose an app, right click and 'display in Finder'.

Here you are in the directory where all apps. You can move them elsewhere or simply delete them. After that iTunes will just warn you it cannot find the app anymore, but at least the deleted apps will not be copied anymore to your Mac.

Of course, you will still have to wait that synchronization copies your newly installed apps to your Mac, but once you've deleted the app on your Mac, it will not be sync'ed anymore.