I was coming here to post the exact same answer, as that is what I did to connect after trying all other options. Since I have them together from posting on another forum, here are the step by step directions for a DIR-655 for those who need a little more guidance to setup WPS:
1. In your router's setting enable WPS WIfi Protected Setup, this is critical or it won't work. I found the settings on the DIR-655 on the menu ADVANCED>Wifi Protected Setup I checked the ENABLE checkbox, then went down to the ADD WIRELESS STATION section at the bottom and noted that there is a "ADD WIRELESS DEVICE with WPS" BUTTON - DONT PUSH IT YET! Keep this page up on your router settings...Pick up your S3 and go to Step 2
2. in wifi settings on your S3, select your router name and click "forget network" to erase all those silly entries you've been trying all day that didn't work. If you did step 1 right you will see on your phone, in the available networks list your router name will have underneath it "Secured (WPS available)" If it doesn't say this go back to #1 and read your router instructions to see how to enable WPS...until you see the "Secured (WPS available)" under your router name.
3. On the same list of available networks on the S3, you see your router name with "Secured (WPS available)" under it - select your router name..
3a. DISREGARD the password field...leave it blank. Dont check the Show Password checkbox. DO CHECK the "Show Advanced Options" checkbox. Go to step 4
4. You will now see that there is an option in the Show Advance Options dialog called WPS, and it will say "OFF" click on this and I used the PUSH BUTTON option, in your router's WPS settings there should be a ADD WIRELESS DEVICE Push Button option <this is the page you left open in your router menu in step 1>, you click the button on both the router and the phone and they start talking to each other! The router configures the phone to work on the router...when done my S3 FINALLY said it was connected, and it's been working beautifully since.
4a. If you don't see WPS as an option...then you don't have WPS enabled correctly on your router, go back and recheck the instructions for your router on how to enable WPS, which is Wifi Protected Setup.
4b. You can Use a PIN instead of the Button option, where you pair them using the same pin number, I had two pin choices on the S3 menu and didn't feel like reading what the difference was so I just went for the button option simply because...it was easy.