Access webcam without Flash

I want to create a video chat application using HTML 5 elements and JavaScript, and I don't want to use Flash to access the user's webcams.

How can I accomplish this using only HTML and JavaScript?

At the moment of writing this the best solution is WebRTC. It is supported in Chrome, Mozilla and Opera, but still unavaialble in Internet Explorer and Safari.

Minimalistic demo.

Index.html

<!DOCTYPE html>
<head>
</head>
<body>
    <video></video>
    <script src="webcam.js"></script>
</body>

webcam.js

(function () {
    navigator.getMedia = (navigator.getUserMedia || navigator.webkitGetUserMedia || navigator.mozGetUserMedia);

    navigator.getMedia(
        // constraints
        {video:true, audio:false},

        // success callback
        function (mediaStream) {
            var video = document.getElementsByTagName('video')[0];
            video.src = window.URL.createObjectURL(mediaStream);
            video.play();
        },   
        //handle error
        function (error) {
            console.log(error);
        })   
})();