...well, not quite yet. But I know some Japanese scientists who can.
In their experiment, the researchers showed people the six letters in the word "neuron" [the name of the journal where the study was published] and then succeeded in reconstructing the letters on a computer screen by measuring their brain activity.
So far, they've only managed to read simple images using 400 background information scans, so think complex thoughts and you should be safe.
Imagine how freaked out people would have been if this paper had been released in say, 1992, at the height of Crichtonism (the insane fear that the Japanese would soon own America, body and soul, most perfectly realized in Michael Crichton's anti-Japanifesto Rising Sun.)