I'm seeing vague and conflicting reports on the web.
Supposedly, the 60D and T3i both allow you to hook up a USB hard drive and shoot directly to the drive without using an SD card.
If this is true, second question: Does it work with HD video recording?
Supposedly, the 60D and T3i both allow you to hook up a USB hard drive and shoot directly to the drive without using an SD card.
Your information is incorrect, there is no support in either the Canon 60D or the Canon T3i for being able to hook up a USB drive directly to the camera and shoot directly to it (still photographs or video) without some intermediate hardware in between (read: a computer).
If this is true, second question: Does it work with HD video recording?
Since it is not true, this means that by default the answer to your second question is also 'no.'
CF (Compact Flash) uses the IDE interface, identical to internal IDE hard drives. I have seen mods of equipment using CF to work with HDD's, and this is also how the CF based internal hard drive adapters work (you can buy one for very cheap to be plugged into one of your HDD slots, to speed up disk access. It is essentially just wiring, no electronics required). Given that, I can imagine modding a CF-based camera to work with external drive.
SD is a different story, as it implements a completely different interface. I think there are SD to CF adapters that will let you use a SD card in a CF device, but I'm skeptical that the reverse conversion exists. So, with a SD based camera, your only solution seems to be shooting tethered with EOS Utility.
I don't believe you can record directly to a USB hard drive.
According to Adobe's documentation, you can shoot tethered with the 60D and Lightroom. This would allow you to use a computer/laptop running Lightroom to control the camera and have the files stored onto your computer - or an external USB hard drive - via Lightroom. That same document does not indicate support for the T3i, although older models of the Rebel series are included.
I'm not aware of a way to record HD video in a tethered mode. Edit: Jay points out in a comment that the Canon EOS Utility (supplied with the camera) apparently supports tethered video capture.
Nothing about USB in Canon's specs for the 600D: http://www.usa.canon.com/cusa/consumer/products/cameras/slr_cameras/eos_rebel_t3i_18_55mm_is_ii_kit#Specifications
The other obvious question is also, "how would you power an external HDD" - the camera won't be able to keep a 2,5" drive for long and a 3,5" drive is pointless for portability.
Yes, it does work. There is an application called EOS utility. If you have that application, then you can take pictures directly to your computer. In fact, you don't even have to touch the camera. There is everything on the EOS Utility from the picture button, all the way to white balance. As for video, I'm not entirely sure. I tried with EOS Utility, but it only allows me to record to my card... Although, there must be a way to record video to computer too, probably through something other than EOS Utility. I tried photobooth, but it didn't register my T3i as a camera... I'll keep searching though.
The t3i will not stream to a disk. You can tether your camera to a laptop with the bundled software but it will record to your flash card not the computer. The A/V out cable does not send a signal while recording. Scratch that. It sends a signal equal to the resolution of the viewfinder, not the recorded footage. imovie or photobooth will not recognize the camera as being attached like it would a webcam. Files too large? Wrong format? I don't know of any consumer or prosumer gear that streams high def other than crappy web cams. I am, however, about to try this with PearNote. But I've never been able to get quicktime, FCP, or iMovie to recognize the canon even with the eos utility. Besides I don't think it's sending audio, only video.
