I usually listen to/watch podcasts on my Android devices, but I would like to be able to manage them from a web browser or perhaps desktop app.
This probably means an account in the cloud which stores the information, and which is accessible from an Android app, and with a web interface.
Ideally it should be possible to click links, like with iTunes, or past links from the web.
gPodder is a free, synchronizing podcast fetcher/client which can not only sync subscriptions but even until which position you've already listened an episode.
It's available for Linux, FreeBSD, Windows, Mac OS X, the Nokia N9, Blackberry 10, the Blackberry Playbook, Sailfish OS and Android.
If you use their gpodder.net service or if you install the according web application on your web server, you can also manage your subscriptions in your web browser.
Pocket Casts should fit in your needs. It's a cross platform podcast app with a Web interface to manage your subscriptions and backups.
