C# get process output while running

Is there anyway to redirect standard output of a spawned process and capture it as its happening. Everything I have seen just does a ReadToEnd after the process has finished. I would like to be able to get the output as it is being printed.

Edit:

    private void ConvertToMPEG()
    {
        // Start the child process.
        Process p = new Process();
        // Redirect the output stream of the child process.
        p.StartInfo.UseShellExecute = false;
        p.StartInfo.RedirectStandardOutput = true;
        //Setup filename and arguments
        p.StartInfo.Arguments = String.Format("-y -i \"{0}\" -target ntsc-dvd -sameq -s 720x480 \"{1}\"", tempDir + "out.avi", tempDir + "out.mpg");
        p.StartInfo.FileName = "ffmpeg.exe";
        //Handle data received
        p.OutputDataReceived += new DataReceivedEventHandler(p_OutputDataReceived);
        p.Start();
    }

    void p_OutputDataReceived(object sender, DataReceivedEventArgs e)
    {
        Debug.WriteLine(e.Data);
    }