put.io
You can download our official iOS app here. It allows you to manage your files, stream videos with subtitle support, download video files for offline usage, cast videos to Chromecast, and link your put.io account with our AppleTV and other official apps!
PutioSync
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 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.
Apps that Shall Rest in Peace
PutioCaster
PutioCaster was able to 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. Thanks go to @tonybuckingham.
Putview
This one was an iPad-only app, that also had the ability to download videos for offline viewing. Thank you very much @mxey.
Fetch
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 in 2012. You can still use it as a starter: https://github.com/orta/Puttio