Bob wants to use his Canon Rebel T3i as a webcam. Leo says he would need HDMI passthru. He'll need a miniHDMI to HDMI cable, then he can connect it to his TV. But if his computer doesn't have HDMI, then he'll also need a video adapter. But for all of the effort required, he should probably just get a good HD Webcam. Leo likes the Logitech C920. It'll connect via USB and will work great.
Another reason the DSLR may not be a good choice is that it may time out to save battery life, or the sensor will overheat after about 29 minutes. There's also a strange taxation issue which causes the camera to not record beyond 30 minutes. So all DSLRs cut short recording time to avoid that.