Can I stream video to an Apple TV without using iTunes? iTunes is good, but if I can have another way to stream video, it would be great.
Indeed there is. You can try AirFlick - it encodes video on the fly and sends it straight to your AppleTV. I've used it for a while now, and although it can be a little unstable from time to time, it really is very useful.
Of course, you could always install XBMC following this guide and control it, play all sorts of video, and make tons on neat customizations however you see fit.
Airvideo is another option, but requires another iOS device to act as an intermediary between the atv and the machine where your video is stored.
Firecore is brilliant, it allows almost any sort of video to be streamed from a networked drive directly to the ATV without the need for ANY intermediary device (I have only tried it with a Time Capsule). BUT it requires a jailbroken ATV and is currently in Beta. Easy install with a very simple bundled jailbreak package. Still, does away with the need for iTunes or an 'always-on' computer.
I use Beamer ($19.99, free trial). It's got a flat, Yosemite-native theme, and is 100% reliable if your network and the AppleTV on it are configured correctly. Dragging files to the Beamer icon will immediately start playback on the AppleTV.
It works with every format except WMV that I've run into thus far, including DivX, MKV, and all the native video types. In addition, you can play, pause and scan using either the AppleTV IR remote or the app window, which I thought was a pretty nice feature.
If you have an iPad, it can stream to an Apple TV via AirPlay.
AirPlay works with any app that supports it, including Video, Pictures, YouTube, and others. I've even seen workout apps that stream how-to videos.