Sites like omegle.com want video from my connected camera, but I don't have one. How can I feed omegle.com (a Flash app) a spoofed video feed (eg, a static picture, mp4 file, etc?)
CamTwist creates "pseudo-video" devices for lots of different things, so you could display your desktop or any subset of it, or other content you choose. CamTwist's feature set is likely very similar to Ryan Sharp's suggestion for ManyCam.
iGlasses is one way to do this. It shows up as a camera on websites, and you can play a video or show an image by dragging it into the effects tab.
Theres a free application called ManyCam, I've used it on Facebook and ChatRoulette to display a picture or movie file instead of my iSight.
I have java applet for spoofing the chat, you can see both parties chat and hijack the chat, but you can't spoof the webcam with it. If you know java, i can provide you source code. It may help for your research in order to get what you need for spoofing.