So I've been doing a ton of research on this over the last couple of weeks since I got my Note 3. I've been wanting a nice pair of on-ear cans (I hate earbuds) that had included in-line controls for volume and track skip/pause/answer calls, stuff like that.
And I came up empty. Nothing. There is literally no third party on-ear headphones with a remote that works with Android phones. Everything is made to work natively with iOS devices. I DO have a pair of Klipsch S4A earbuds that were designed for Android, but like I said, I hate earbuds, they are uncomfortable, I cannot get a good seal on them and they sound like garbage. I ultimately decided that I wasn't going to find wired, portable, on-ear cans with an Android-compatible inline remote. So I ignored that feature set and focused more on audio quality for the price point I was looking at ($199 or below).
So I settled on a pair of Sennheiser Momentum On-Ear (they have a larger, Over-The-Ear model for $100 more, but I picked up the smaller On-Ear model). It comes with a three-button inline remote with mic that I wasn't expecting I was going to use, because they do include a straight cable sans remote as well. Plugged it in with the in-line remote cable and it sounded fantastic and was very comfortable. So the deal is, I'm actually getting *partial* functionality with the remote. The two volume buttons do not work, but the middle "multi-purpose" button does, without any extra software too. A single press will pause/play. A double tap will skip to the next track. Holding the button for 2 seconds opens up S-Voice. And the mic on the remote also works flawlessly. When a call comes in, pressing the button will answer the call, and holding it in will reject it.
I think this functionality is the most anyone is going to get out of a third-party set of wired cans. Even the S4A's don't have volume up/down, instead relegating that function to the same single-button setup. It's not perfect, but it's functional.