How can I stream webcam video with C#?

You could just use VideoLAN. VideoLAN will work as a server (or you can wrap your own C# application around it for more control). There are also .NET wrappers for the viewer that you can use and thus embed in your C# client.

The usual API for this is DirectShow.

You can use P/Invoke to import the C++ APIs, but I think there are already a few projects out there that have done this.

http://channel9.msdn.com/forums/TechOff/93476-Programatically-Using-A-Webcam-In-C/

http://www.codeproject.com/KB/directx/DirXVidStrm.aspx

To get the streaming part, you probably want to use DirectShow to apply a compression codec to reduce lag, then you can get a Stream and transmit it. You could consider using multicast to reduce network load.

If you want a "capture/streamer in a box" component, there are several out there as others have mentioned.

If you want to get down to the low-level control over it all, you'll need to use DirectShow as thealliedhacker points out. The best way to use DirectShow in C# is through the DirectShow.Net library - it wraps all of the DirectShow COM APIs and includes many useful shortcut functions for you.

In addition to capturing and streaming, you can also do recording, audio and video format conversions, audio and video live filters, and a whole lot of stuff.

Microsoft claims DirectShow is going away, but they have yet to release a new library or API that does everything that DirectShow provides. I suspect many of the latest things they have released are still DirectShow under the hood. Because of its status at Microsoft, there aren't a whole lot of books or references on it other than MSDN and what you can find on forums. Last year when we started a project using it, the best book on the subject - Programming Microsoft DirectShow - was out of print and going for around $350 for a used copy!