You can help test our official iOS app from here. It can manage your files, stream your videos with subtitle support and link your Put.io tvOS device. Please note that this is a highly unfinished app. We will keep working on it.
PutioCaster can access your put.io account and play your videos either on your iDevice, including the AppleTV, or cast them to your Chromecast, Roku or Xbox One. You can find it at http://putiocast.com
It's free but will require an upgrade to premium ($1.99) to unlock many features, like adding subtitles, downloading for offline viewing or MP4 conversion. Thanks go to @tonybuckingham.
This app will help you manage your files & folders and stream your videos. But there's more: It will also let you download videos to your device to watch when you're offline. All of its features are free. There seems to be no subtitle support and casting to another device is not possible, though.
It's Playing App
This is a full-featured video player which can access to your cloud storage accounts. Thankfully put.io is among them. It can play any type of video and can download and add subtitles from opensubtitles.org by itself. They can also download videos from put.io for offline viewing and since they can play any kind of video, conversion is not a concern. However, you'll need a Pro account to add put.io as a cloud option.
Unify - Cloud File Manager
Unify can access all your different cloud storage accounts. You can manage your files and download them for offline access. It also has super useful features such as previewing and unarchiving ZIP and RAR files and PDF viewing - you can check them all out from here. However, you'll need a Pro version to be able to add multiple cloud accounts and watch the videos that are not in MP4 format.
Apps that Shall Rest in Peace
This one was an iPad only app, that also had the ability to download videos for offline viewing. Thank you very much @mxey.
Fetch was a great universal iOS app that made use of your files metadata. It worked on iPhones, iPads and even Apple TVs.
Unfortunately, it was removed from the App Store for allowing users to add new transfers to put.io. It will be missed dearly.
If you have ever tried it, you can still find it in the "Purchased" tab of the App Store.
The creators of Fetch open-sourced their code: https://github.com/TryFetch/Fetch
If you'd like to modify and submit it to the App Store again, you're welcome to try. :-)
@orta's Awesome put.io app
The first victim of adding the ability to start transfers from the app. @orta's app was removed on 2012. You can still use it as a starter: https://github.com/orta/Puttio