This phenomena may have been explained. The crux of the problem had to do with differing reference frames - the distance traveled according to the satellites which measured the time was different from the distance traveled according to us on earth. If you're going to measure speed (distance / time), you have to get the distance and time both from the same reference frame. We were getting distance from our reference frame and time from the (very fast) satellite's reference time.
This article explains it in a very accessible way:
To understand how relativity altered the neutrino experiment, it helps to pretend that we're hanging out on one of those GPS satellites, watching the Earth go by underneath you. Remember, from the reference frame of someone on the satellite, we're not moving, but the Earth is. As the neutrino experiment goes by, we start timing one of the neutrinos as it exits the source in Switzerland. Meanwhile, the detector in Italy is moving just as fast as the rest of the Earth, and from our perspective it's moving towards the source. This means that the neutrino will have a slightly shorter distance to travel than it would if the experiment were stationary. We stop timing the neutrino when it arrives in Italy, and calculate that it moves at a speed that's comfortably below the speed of light.
"That makes sense," we say, and send the start time and the stop time down to our colleagues on Earth, who take one look at our numbers and freak out. "That doesn't make sense," they say. "There's no way that a neutrino could have covered the distance we're measuring down here in the time you measured up there without going faster than light!"
And they're totally, 100% correct, because the distance that the neutrinos had to travel in their reference frame is longer than the distance that the neutrinos had to travel in our reference frame, because in our reference frame, the detector was moving towards the source. In other words, the GPS clock is bang on the nose, but since the clock is in a different reference frame, you have to compensate for relativity if you're going to use it to make highly accurate measurements.
The original paper publishing these findings is here: Times of Flight between a Source and a Detector observed from a GPS satelite.
Sources:  (Associated Press),  (Guardian.co.uk),  (Original Publication - Cornell University)
Scientists around the world reacted with cautious shock on Friday to results from an Italian laboratory that seemed to show that certain subatomic particles can travel faster than light.
The journey would take a beam of light around 2.4 milliseconds to complete, but after running the Opera experiment for three years and timing the arrival of 15,000 neutrinos, the scientists have calculated that the particles arrived at Gran Sasso 60 billionths of a second earlier, with an error margin of plus or minus 10 billionths of a second. The speed of light in a vacuum is 299,792,458 metres per second, so the neutrinos were apparently travelling at 299,798,454 metres per second.
Ignoring the boilerplate media hype about the possibilities of time travel and alternate dimensions - I'm looking for academic sources that might suggest how this could be true, or alternatively, how this discrepancy could be accounted for.
I read the published article, Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, with their findings. It looks like they took an insane amount of care with their measurement of distance and time.
One of the most common skepticism of people who no nothing about the experiment is stuff like:
You might worry about[...] have they correctly accounted for the time delay of actually reading out the signals? Whatever you are using as a timing signal, that has to travel down the cables to your computer and when you are talking about nanoseconds, you have to know exactly how quickly the current travels, and it is not instantaneous. 
This experiment doesn't use that sort of 'stopwatch' timing mechanism though. There is no 'T=0', and no single firing of neutrinos. What is detected is watermark patterns in the steady stream of particles. The streams at the input and output are time stamped using the same satellites and any position along each stream has a precise time associated with it. By identifying identical patterns at input and output streams, they can identify how long it took particles to travel between the points. 
As for distance, they use GPS readings to get the east, north, and altitude position along the path travelled to great precision. So much so that they even detect slow earth crust migration and millimetres of changes in distance between source and destination when something like an earthquake occurs. When your particles are travelling on the scale (730534.61 ± 0.20) metres, this is more than enough precision:
It's going to take a lot more than grassroots skepticism to think of what could have caused this discrepancy. I've seen suggestions such as the gravity of the Earth being different along the path of the neutrinos, which warps space/time unevenly. The neutrino might not actually be travelling as far as they think if space/time is contracted at one or more points along the path where gravity varies.
Anyway, I'll be interested in seeing how it pans out. Like most scientists, my guess is an unaccounted for systematic error (because they definitely have statistical significance and precision on their side) that has yet to be pointed out, but it probably won't take too long with all the theoretical physicists that will be pouring through this experiment.