Adding up to trrlightning reply, in case you need to get rid of a specific application for good, you need to delete it from iTunes as well. The reason why you should delete the application from your iTunes is to prevent it from being copied once more to your phone when you connect it to iTunes for further synchronization.
If you wish to keep the application on your iTunes, however, and you do not wish to have it placed back on your phone whenever you connect your phone to iTunes, you can stop iTunes auto sync.
Hope this helps!
I am able to remove applications that I added to my iphone4, however the applications that were already loaded on the phone do not have an x in the left hand corner. Unfortunately, the stock market ticker continues to update and drains my battery in 2 hours. Has anyone had luck in removing these apps?