Responsive is probably the biggest move forward with things that's for sure! Years ago it was "Fluid Design" in which people were able to make things 100% width, but that can really mess things up with the larger monitors.
Another thing that made it's mark is HTML5. It was finally approved and is now a W3C Candidate Recommendation as of December 2012. This has been a HUGE change moving forward and will see all websites moving in this direction.
According to the timeline for W3C, HTML5 will become the recommendation for 2014 - if you haven't started learning it, it's time to get on the train, it'll be moving fast here very soon!