Paranoia is indeed good. Most people should be a lot more paranoid than they are (have you read the news lately?). Two things to remember:
All computers, all devices, all hard drives will die some day. Every one of them. There are no exceptions to this axiom, it is a basic, foundational truth. That device/hard drive may last a long time, or it may fail right when you need it most. When that day comes, you better have a good, available backup/alternative that works.
Online services and accounts get compromised. They get hacked, they shut down without notice. One would be wise to assume that every online account and service will get compromised eventually (because few haven't).
Personally, I put all my documents on my home computer. Each trip gets its own place (I maintain places for previous trips and future/potential trips). That computer has multiple backups (backups are automated so they require me to actually remember to run them). I also have print-outs on paper of all important travel documents.
Before a trip, I copy every important document to multiple places: a PDF version of every document gets printed out (2 copies, one booklet goes with me, another booklet goes to my wife). An electronic version goes on my iPad, my phone and my wife's phone. Everything (and I do mean EVERYTHING) is always within reach, electronically and in our paper "trip booklet".
Yes, this adds a task. But I have found that it's not terribly burdensome, and it completely eliminates most of the stress. Everything about our trip is immediately and easily available, everything from receipts and confirmation documents, flight details, each day's plan, to the hotel's GPS coordinates - it's all immediately available. It eliminates all sorts of hassles and headaches. You do have to be disciplined to ensure you record every detail as you start booking and planning things, but doing that makes me feel good.
I keep multiple devices backed up, but prefer not to put things online, since having access to the internet is not always available while traveling, and there have been many times when I needed something quickly but had no internet (eg: immediately upon landing in a foreign country). I also have credit card/bank info that I do not want to trust to online services (email is NOT a secure place to store or transmit anything you don't want compromised).
Bottom line: Save everything. Keep it well-organized. Keep it backed up. Get it in a form that can travel with you, and have multiple ways to get that info and keep it at hand.
Paranoid? Who, me?