Beyond Full-HD with Canon EOS 600D?
If you do the math, you will find that a full-res video would need to process too much data per time - 22Mpixel x 30 frames x 3x14 bit color depth = 3+ GByte/second (done in my head, double-check!)

The camera sensor is probably able to provide this data, but neither the in-camera chip nor the memory card is able to process such a data stream fast enough; and the buffers would be full after 2 or 3 seconds of video. Therefore, the camera makers chose to not offer this mode.

I guess if you hack the camera software, you could it make record on that resolution for one or two seconds.