iTunes now shows you which Apps, Books and Music you have already downloaded without need to check your previous purchases.
If you look at the attached screen shot you can see the Top Apps, if you look closely you can see that it already shows NHS Direct as Downloaded, that is because I have it in my iTunes library on the computer.
If you look at the Simpsons Game you can see that it available to be downloaded, this is because I downloaded it in the past but have since removed it from my iTunes Library.
This also works in the paid apps screen and any screen where you would see the 'Buy' button you now see either 'Download' or 'Downloaded' you have previously purchased the item.
If you look at the attached screen shot you can see the Top Apps, if you look closely you can see that it already shows NHS Direct as Downloaded, that is because I have it in my iTunes library on the computer.
If you look at the Simpsons Game you can see that it available to be downloaded, this is because I downloaded it in the past but have since removed it from my iTunes Library.
This also works in the paid apps screen and any screen where you would see the 'Buy' button you now see either 'Download' or 'Downloaded' you have previously purchased the item.