* VEVO (Android, iOS) - music videos app, available in a few countries: Australia, Brazil, Canada, France, Germany, Ireland, Italy, The Netherlands, New Zealand, Poland, Spain, UK and US.
* Red Bull.TV (Android, iOS) - videos and shows
* Songza (Android) - music streaming, online radio (there's an iOS app, but it doesn't support Chromecast yet)
* PostTV (Android) - news from Washington Post
* Viki (Android, iOS) - "Korean dramas, Taiwanese, Chinese and Filipino dramas, Telenovelas, Japanese dramas and anime, American cartoons, NBC Universal, History Channel, A&E, E! TV shows, as well as movies from Indonesia, Hong Kong"
* Revision3 (Android, iOS) - shows
* BeyondPod (Android) - podcast manager
* Plex (Android) - media player, Chromecast support only for videos, the app costs $5 (there's an iOS app, but it doesn't support Chromecast yet)
* Avia (Android) - media player, Chromecast support for local videos, music and photos, requires an in-app purchase that costs $3. I tried the app and it works well for local files, but the Google Cast API supports a small number of file formats
* RealPlayer Cloud (Android, iOS) - movie player that stores your videos online, US and Canada only
"There's no need to huddle around small screens when you can share your own photos and videos using your phone, tablet, or laptop," mentions Google.
From what I tried, the most interesting apps seem to be Songza (for playing online music) and Avia (for playing local files).