In this video from alandeklerk he shows us how to get rid of applications on Facebook which clutter up your page. Click on the application, click Allow. Click on the application name on the bottom left. Now you'll see on the upper left it will say Block Application. Click on that, then a box will come up asking if you want to block it. Click Block and the application will now be blocked. You will not see this on your profile anymore. Do this process for any application you would like blocked forever. You can also hover over a post on your page until Remove pops up and click that to remove it off your page. That won't officially block it, but it will remove the message from your page.
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