As someone who just runs an Ubuntu 14.04 desktop machine without any web server should I be concerned? I don't really see how anyone could remotely execute bash on my system.
Is it connected to the internet? Then patch it. While you can't think of anything that could remotely execute it, you'd be damn surprised how large the attack surface is for this exploit, and how flexible it is. It's a Big Deal(TM). Everything in a Linux system uses bash (hyperbole, but not too far from the truth), and all it takes is one of those not sanitizing input and it's game over :(
Basically, it may not be as immediately exploitable for desktop systems without a web-server as other bugs have been, but I wouldn't be surprised to see something pop-up in the near future.
Yeah, the annoying thing is it sounds like there isn't a full patch yet and new vulnerabilities are being discovered. Just trying to understand if I should shut the machine down until everything is sorted out.
There's no need to shut it down. If you're concerned for some reason (if you have important data on it and/or use it on untrusted networks), just remove bash or at least make it unexecutable.
A fair bit of warning though that some scripts might break, but at least you know why (if the alternative is to turn off the machine until you trust bash again then you may have to wait forever).
On a standard Ubuntu or Debian most shell scripts uses dash anyway so it shouldn't be too bad.
The ecosystem of linux software that shells out to bash is ridiculous, and coercing an env var is a very light requirement.
Virtually any software that takes input from the internet can be a target, and enumerating the combination of versions and configurations is futile. We all need a working bash patch.
Not running a webserver protects against GET spray-n-pray, but you shouldn't feel safe.