Are there any websites where I can setup up a live webcam feed that can be password protected so that only I can view it?.
I've used http://www.ustream.tv before.
When creating your "show", there is an option in the advanced tab for requiring passwords.
Most standalone IP cameras provide such website by themselves. If you have a webcam that works only through the computer, I doubt such thing will be possible without having some service running on your machine.