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!
I agree about responsive design. Mobile browsing is increasing more and more as time goes on. It used to be that you could safely assume not many people would be viewing your site on a mobile browser, but now that is not a viable assumption to make. It is more likely that many of your visitors will be visiting on a mobile browser, so you really have to be prepared for all eventualities.