I've been experiencing severe problems with Apple News on IOS 9. So far it has only happened on my older iPad 2, never on my phone, but as I much prefer News on the iPad, it's quite annoying.
The symptoms are that News starts, is frozen for a bit, and then the Home Screen reappears. It isn't crashed: if I double tap on the Home button, it's still sitting in memory, but selecting it just repeats the same results.
Sometimes these will fix with the usual methods: swipe it out of memory or swipe it out of memory and reboot. However, sometimes that doesn't work either. Another trick I've used is to swipe it out of memory, do a hard reboot and then use a link like A.P. Lawrence Apple News to wake it up. But even that hasn't always been succesful; I once had to completely reset all my iPad content and data to get News working again.
With most apps, uninstalling/reinstalling is often a fix. Stupidly, Apple doesn't let you uninstall built-ins like News. There has been recent talk that eventually they will allow that, but right now the only way to do it is to jailbreak your phone.
A slightly less draconian fix is to go to Settings->iCloud and turn off News. It then asks if you want to delete data stored on your iPad. Do that, then turn it back on. That works and your Favorites are not lost.
I've had less problems with my iPhone 5s - News does freeze now and then, but so far swiping it out of memory fixes that. However, News on iPad is much better because of the screen space.
Really, Apple, shame on you. If you can't make this work right on older equipment, then don't release it for those platforms. That's especially true when it's something with real promise that people enjoy greatly. Screwing up something good is far worse than not producing it at all!
Update 9/26/2015: this morning I installed the latest update from Apple. News still crashes.