Try that if you're one of the folks checking into a hospital right now up there in the northeast, in the electricity void following storm Sandy.

Luckily, hospitals are required to treat your true emergency conditions with or without insurance. That all gets sorted out later.

I can't imagine any hospital allowing you to insert a thumbdrive into one of their computers. If they do, and it actually works, their I.T. department is a bunch of idiots. They may even block you from accessing cloud storage, but I don't know about that. At least using one of their in-hospital computers all this should be blocked, and they should not even allow you to touch one of their in-house computers. They may have DMZ computers, off their LAN, that they will allow you to use. But with the advent of smartphones and the ability to access the internet via 3G/4G, the need for a dedicated computer is diminishing for some things. For things like insurance numbers, why not encrypt them right there on your smartphone? Adding cloud storage into the picture just makes you dependant on another layer of technology maintained by a third party out of your control.

I use a paranoid approach:

1. Main storage is a server using a RAID array.
2. I use robocopy to copy data to a workstation with a larger hard drive using a scheduled task. Here is a link if you are interested in the free tool from Microsoft: http://www.microsoft.com/en-us/download/details.aspx?id=17657. Way better than xcopy.
3. I use cloud-based backup service
4. I use robocopy to copy data to an external hard drive using a scheduled task. The external hard drive is located on a shelf positioned right by the most likely fire egress door. I call this my 'run for your life' backup.

I also make it a habit to clone and replace hard drives every three years in my server. I just recently started moving my workstations to solid state hard drives.

IMO, for backing up it's best to have multiple strategies rather than relying on one strategy.

One is none, two is one...

Funny....and true.
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I can't imagine any hospital allowing you to insert a thumbdrive into one of their computers. If they do, and it actually works, their I.T. department is a bunch of idiots.

Yup,get ya fired on the spot.

At a minimum get on-board with a free backup system -- don't loose your files.

The replies here are excellent (as usual!) but they are mostly tactics, not strategy. Establish a strategy first, then select tactics to achieve that strategy. Nailing down the right strategy helps you 1) discover threats you didn't think of and 2) avoid wasting resources on poor tactics. It takes a little more up-front effort but the payoff is worth it.

A good example of a valid strategy (followed by tactics) is Listening to Katrina. Use it as a starting place, not gospel, then decide on YOUR strategy and follow up with appropriate tactics.

I agree you should have the numbers on your phone and in your wallet - this is much quicker than looking them up online. But I like Google Docs, DropBox, etc. for keeping a backup copy in the event you are without wallet/phone. Most hospitals have Guest WiFi and I can't imagine I couldn't find someone in the room to lend me their phone/laptop for 5 mins to look it up.

While I agree with your InfoSec standards my IT consulting time says most businesses are overwhelmingly wide open (including many major hospitals). :-(

For a strategy start by risk ranking your information, i.e. decide what is most valuable to you.
I have an Accounts folder that gets backed up, it has my spreadsheet where I list each bill and when I paid it on a 12 month grid as well as a budget based on those, then subfolders with statements and documents from each.
Then a personal folder for each person which has their medical records, school records, individual accounts, etc.
Then the pictures, music, etc like most people have. Then an Archive folder, if you change jobs, or close an account then those subfolders move under Archive.
So priority 1 is the accounts and personal, then priority 2 is the pictures, music, archive. Then priority three are things I could recreate such as Reference which are documents downloaded from the internet or the virtual machines I test things on or the general Downloads folder.
Priority 1 stuff gets copied to a pair of drives in USB enclosures,one online on the server the other in the safe, going to add the third back in shortly for the offsite. Those Priority 1 folders also get burned to a DVD and stored with the paper version of them in the important documents binder in the safe as well as offsite. I actually have a bluray burner but since I don't have another bluray reader at my home or my parents home yet I still burn on dvd's.
Another strategy is to ensure data is in as open format as possible, no issues accessing data due to a program not activating or new versions not supporting the old file format after an upgrade. So my spreadsheets are done in OpenDocumet format for example.
My electronic copies are organized the same way as the paper so I could easily make a copy of the whole important documents binder by opening the master document and printing it. Originals are color scanned and linked into the master and the paper version is organized similar with one section for the shared things and one section for each person.
Then I always have more than one laptop, if we buy ourselves a new one the old one becomes the file/backup server. Should we loose one laptop the old is kept up to date so we could just use it to access the backup copy of our data.