GNOME Twitch [github, Official Site] recently released a major new version of their open source desktop Twitch client and it's a beauty. The new version includes: Notifications of when people you follow go live, Language selection in the menu to filter livestreams, chat badges, viewer count for games and more. See the changelog here.
I much prefer it to using Twitch in a browser personally, since it's faster and I get better quality and the overall feel is much nicer than a browser window. One thing that is missing is the actual viewer count on each channel, something I would like to see. Also, the ability to see who is in the channel chatting too, a list would be nice. I actually requested these features and the developer was very receptive, as they plan to include such features in the next release.
There's other tools like "Streamlink" which will enable you to view a Twitch stream in your favourite desktop player.