Iphone 6+ and iOS 9.0.1 with approximately 30% free space in storage.
After updating to 9.0 and 9.0.1 I've experienced my touchscreen locking up, apps locking up, and the double-tap home screen not working on an unfortunately regular basis. I can't swipe up to close apps because the touchscreen doesn't work. Pressing the home screen button gets you to the home screen, but you can't swipe or select anything. I have to press the power button to go to standby, then press power again and manually enter my code and unlock the phone. Touch ID doesn't "clear" whatever the glitch is. Then things work normally - until the next glitch. This happens several times a day. I've done a full factory reset/restore to 9.0.1 as a "new" phone, then re-added all of my material and this is as good as it gets.
Prior to the reset/restore with 9.0 and 9.0.1 the touchscreen would lock, stutter or generally refuse to accept any input. Doubletapping home screen wouldn't bring up anything, it had no effect other than taking you to the home screen. The touchscreen would be inop, Most apps would lock or crash. Hands down the worst iOS update I've had to deal with since owning an iPhone. The only thing that would work to get the phone operating properly would be a hard reset and oftentimes that lasted less than a minute until the next lockup.
Unacceptable for a device less than a year old for the premium that Apple charges.