Well, it may be two months too late but I've found my favourite movie sequence of 2013. In my defence, I only saw the supplying film, Disney's Frozen, yesterday.
The sequence, as anyone who's already seen Frozen may have guessed, is the "Let it Go" musical number. It's up on Youtube - I was going to post it here, but it really needs to be seen a) in the context of the whole film and b) on the biggest screen possible (and probably in 3D, unfortunately I could only get to a 2D screening). It's basically a perfect storm - great song, stunning vocal performance (both technically and emotionally) from Idina Menzel, and some utterly astonishing animation. And by astonishing animation I don't mean the ice powers (although they're great) - I mean the actions, reactions and emotions of the character Elsa. Rarely if ever have I seen such a jawdropping example of animated acting. The moment where she throws her crown away and lets her hair down is just incredible.
The rest of the film has a few flaws (the script feels underdeveloped in places, some of the songs are notably weaker than others) but overall it comes recommended. Even if you just watch it for that four-minute sequence.