Have any of you tried the Mindstorms EV3 and if so, what are you using to program it?
My FLL team this year used the EV3. The only (sane) option to program it is the software that comes with it (very similar to the NXT version, but cleaned up and with some functionality added).
Depends on if you’re using it for competition or not.
For FLL, you can really only use the EV3 software.
For non-FLL purposes, ROBOTC is coming out (or has come out) with an update, I believe that the people behind Brixcc are working on an update as well. Of course, interfacing with the Linux environment directly through C or similar is always an option. 
I was part of the study group during the last year of development. I think the software is a big upgrade to the NXT. There are some great updates that make it easier to use in the classroom and easier to transition from WeDo.
You could still use NXT in FLL this year.
Do you know anyone who has actually done this? I see some places where people try things like running their own Linux distro on it, like here: http://botbench.com/blog/2013/10/28/breathtaking-debian-wheezy-on-the-ev3/. But I haven’t been able to find any documentation about how to even turn on a motor.
I downloaded the software from the LEGO website and looked at it very briefly. I haven’t looked at it in enough depth to have a solid opinion of it. I wish I had enough time to play with it some more.