I am looking to be able to use my Canon EOS Rebel T3i as a webcam on a computer, both Mac and Windows based. Some uses for this would be a HD live stream or the ability to record video directly to my computer. I know I would need to use an HDMI cable to connect my T3i to my computer. Since there is no HDMI in on the computers I will be using (or any computer that I know of) I would need a way to connect my T3i's HDMI out to my computer. I am looking at the Blackmagic Design Intensity Shuttle for USB 3.0 and the elgato Game Capture HD. It needs to be able to work with USB 2.0, as that is the only port that I have on both of the computers I would be using this with. The elgato runs from USB 2.0 and where the Intensity uses 3.0. I need to know 100% that the Intensity would work on 2.0. I also need to know if they would show up as a webcam on the computer. The apps I would be using would be Skype, EasyWorship, and an Twitch.tv.
You can probably do it directly through the EOS software. It is possible to get a live video stream from the camera over the USB connection. Note that USB2 is not going to be able to carry a full quality HDMI stream though. This is why the Intensity is USB3. It requires USB3 because the bandwidth requirements for the quality level it is working at require USB3 data rates. If you have a firewire port on both, that would be an alternate option.
There are systems that have HDMI capture, but they are due to having an encoder card like the internal version of the Intensity. If it is a desktop that doesn't have USB3, it may be possible to get a USB3 card for that system. I personally have used an addin card for USB3 support on my desktop (a first gen i7) and it works great.
No matter what you do, there is a good chance you are going to have to hack your way to getting it to show up as a webcam. It would likely show up as a capture device though, which should work with EasyWorship or ProPresenter. (Personally I'm an old MediaShout fan that is looking at swapping to ProPresenter since Media Shout went pretty awful with version 4, but I've used all 3.)
One other option you haven't considered is that there may be a way to use the USB connection to pull the LiveView feed that EOS Utility uses, but it still wouldn't be as good of quality as something like an Intensity, but free is good and it would likely support USB2.