Facebook Mass Accept Requests is a Greasemonkey script for Firefox that will allow you to "accept all" on your page of requests. Once you have this browser addon installed, it will add checkboxes beside each one of your requests so that you can choose to accept whichever ones you like. After that, clicking a simple "accept all" button will automatically go through and accept all of these gifts. In some games, it can even send back a reciprocal gift.
This doesn't work for all games 100% of the time, so your results may vary. It is known to work well in FarmVille, Farm Town, and FishVille. Other apps that don't work too great are Mafia Wars, Cafe World, and Social City. You may have to try your favorite game and report back and let us know which work and which do not.
Installing a Greasemonkey script is actually pretty simple, as long as you have Firefox installed. Greasemonkey is a simple browser extension that you can install by clicking here. After you have installed Greasemonkey and refreshed your browser, install the Facebook Mass Accept Requests script by going here. Click the install button and it will now be loaded. Simply go to your Facebook requests page and you should now see a new "Accept All" button. Give it a try.
Have you tried this out? Tell us about your experience in the comments below.