How can I get a running sum for a list?

I've got following data I'm reading from a file:

data = {{{2013, 1, 11}, 4},
   {{2013, 1, 12}, 1},
   {{2013, 1, 14}, 1},

   {{2013, 1, 16}, 2},
   {{2013, 1, 18}, 1},
   {{2013, 1, 19}, -1, 16},
   {{2013, 1, 20}, 2},
   {{2013, 1, 21}, 2}
   };

(notice that list elements may have an extra item.) Now I want a similar datelist with each time the accumulated sum (ignoring possible third elements after a data item, like the 16 in the example). Procedurally I'd do something like this:

tally = 0;
datelisttally = {};

For[i = 1, i <= Length[data],
  tally = tally + data[[i]][[2]]; 
  datelisttally = Append[datelisttally, {data[[i]][[1]], tally}]; i++];
DateListPlot[datelisttally, PlotRange -> {0, Automatic}, Joined -> True]

but I'd like to learn the best way to do this with functional programming, best being the fastest. (The file may hold several thousands of items.)

update
I've benchmarked the 3 current solutions, and these are the results (list length = 1 million elements, averaged over 50 runs):

• Szabolcs's: 0.33 s



• PlatoManiac's: 0.54 s


• Leonid's: 3.33 s

Answer

One (not functional) possibility out of many:

dataacc = data;
dataacc[[All, 2]] = Accumulate[data[[All, 2]]]

This will keep the third elements. If you want those removed, you can start with dataacc = data[[All, 1 ;; 2]];

I didn't benchmark, but I expect this to be fast.