Jeremy Blythe has a fair number of Raspberry Pi projects under his belt, including this one, which displays a simple webcam stream on a web page. It is an ideal setup for a baby or child monitor, and it’s a good starter project because it uses out-of-the-box components and doesn’t require any hardware engineering. You’ll need a webcam, though.
The project runs on a headless Raspberry Pi, which means it’s set up to work without a screen or keyboard, so Jeremy used a secure shell connection (SSH) to access it. It’s relatively simple to load up the two main applications: MPlayer (a Linux movie player) and Motion (as a streaming server).
See Jeremy’s blog post for the detailed instructions, and links to other projects: