Like others, I have been getting this same problem. I have tried formatting a new, good quality micro SD card using two computers with Windows 7 (64 bit and 32 bit); a combination of adapters as well as a native computer SD slot and a SD card holder. In every case, I have used the SD Formatter program as recommended, with various options set or not. None of them worked! Every time, when I tried to boot into the Raspberry Pi, I got the same error message 'Error resizing FAT partition'. It also didn't seem to matter if I extracted the NOOBS files to the SD card after formatting; if I extracted them to a separate directory and then copied them; if I safely removed the SD card and then reinserted it after formatting - generally, all of the so-called fixes mentioned here just did not work. However, the one trick that did work was to put the SD card in my camera; format it (it takes about 10 seconds!); put it back on to the computer and then copy the files from the previously extracted NOOBS directory. And it works! Not only that, it takes about 3 minutes from start to end instead of the 30 to 45 minutes using SD formatter. So my inescapable conclusion is that there is something wrong with the SD formatter program. Forget all the other 'solutions'. Grab a camera (mine is a Canon, but I'm sure any reasonable camera will do); format the card in it; extract the NOOB zipped files to a directory; copy them to the - now correctly formatted - SD card and all should be good.
