The most tested incremental update in the history of iOS is ready to download an install.
I haven't heard enough from people with older devices to give you s definitive answer, but if you are already on iOS 9.2.1, there is probably no good reason not to upgrade. Those of you still on iOS 8, as always, maybe wait a bit and we'l see what the pioneers report from the front. Certainly, if you have a 6S or a 6, go ahead and upgrade to 9.3 and enjoy the new NightShift feature which may help you sleep better if (really, IF?) you use your device at night. The last two generations of iPad should also benefit with no downside.
Here's my recommended method for every iOS upgrade:
1. Save all your photos and videos to the cloud or to your computer. There's no sense risking losing them if anything goes wrong, and they're taking up space that could be needed during the upgrade. My practice is to have copies in the cloud and on a hard drive.
2. Remove the apps you never use. It will free up space and declutter your home screen.
3. Make a backup. Check your backup. Your device should be backing up to iCloud every night, but it's a good idea to check, and make sure that you have a current backup. I strongly recommend connecting your device to your computer and making a backup to it using iTunes. It's a more complete backup, and if something goes wrong, it's a lot quicker to restore from iTunes than to restore from iCloud. (I speak from experience. Trust me.)
4. If at all possible, do your update via iTunes. The over the air updates seem to be OK these days, but again, in the event of complications, having the computer and iTunes handy can make for an easier recovery. If you are tight on space on your device, the iTunes update is definitely less of a hassle.