Invis' Monk Build
One of the best Monks in the world - Invis, has been using a very mobile Lashing Tail Kick + Epiphany build, which he does great things with in cooperative play. You can even see the build currently being used live on his stream!
Lastzoul's Fire Monk
Lastzoul's Monk build is aimed directly at Torment 6 farming. Of course, the skills are the most important part, but you should check out his video as well in order to get a better view of the build. He came up with it before RoS came out, but everything still works the same way right now.
Stun Lock Monk
While he usually plays on the console YouTube user fiveonethreeV1 has moved to PC for Reaper of Souls and has made a video guide for a Stun Lock Monk. You can check out the entire video here, where the author goes through his gear and explains his choices for it.
Bagstone's Pure Tank Monk Build
Bagstone made some modifications to his Pure Tank Monk Build and is now looking for feedback, aside from hoping to be useful to other fellow Monks. So check his topic out and share your thoughts if you've tried it out or if you've got theories without having to test it.
Netherfrost's HC Lightning Monk
You know we've featured Lightning builds in the past (you can see them in the Builds section), but Netherfrost's thread deserves special attention not only because of the build, but because he's created a whole guide, named "The Eye of the Storm - A Lightning Monk's handbook". He even links different builds for soloing and for playing in a party. There seems to be everything needed in the post - gear, Paragon points, play style, and much more!
[Guide] The Fire Monk 2.0.4
Raisuun has created a fire Monk guide that has some very nice depth and detailed explanations to it. The build uses Lashing Tail Kick for its main source of damage and relies on a good balance between offense and defense. There's also a nice guideline on the item stats you'll require to make this work.