How to remove apps from iTunes?

I sync my iPhone 4s with iTunes. In the past (way back in 3Gs days), I tried a bunch of apps, then removed them from the phone, since I didn't need them anymore. However, for reasons unknown, they are still in the list in iTunes. Note the screenshot:

For instance, I no longer use DeepFish and Bubble Ball, but they are still in the list. How do i get rid of these apps?

Yes - just delete the apps from your Library on iTunes and they won't show in the list of apps that could be synced.

The long version is click on Apps in the Library, then select one or more apps and press the delete key. Answer a few dialog questions to confirm you want to delete and move the file to trash (or not) and you are done. The next sync will remove that app from your iOS devices.

Do note, that if you don't sync for a while, the iTunes could see the apps on the device as new and needing a transfer back to your library, so be sure to sync sooner or just pay attention when a "items were found on your device" dialog pops up and asks you to transfer purchases back to the library.