How can I read an Http response stream twice in C#?

Copy it into a new MemoryStream first. Then you can re-read the MemoryStream as many times as you like:

Stream responseStream = CopyAndClose(resp.GetResponseStream());
// Do something with the stream
responseStream.Position = 0;
// Do something with the stream again


private static Stream CopyAndClose(Stream inputStream)
{
    const int readSize = 256;
    byte[] buffer = new byte[readSize];
    MemoryStream ms = new MemoryStream();

    int count = inputStream.Read(buffer, 0, readSize);
    while (count > 0)
    {
        ms.Write(buffer, 0, count);
        count = inputStream.Read(buffer, 0, readSize);
    }
    ms.Position = 0;
    inputStream.Close();
    return ms;
}

Copying the stream to a MemoryStream as suggested by Iain is the right approach. But since .NET Framework 4 (released 2010) we have Stream.CopyTo. Example from the docs:

// Create the streams.
MemoryStream destination = new MemoryStream();

using (FileStream source = File.Open(@"c:\temp\data.dat",
    FileMode.Open))
{

    Console.WriteLine("Source length: {0}", source.Length.ToString());

    // Copy source to destination.
    source.CopyTo(destination);
}

Console.WriteLine("Destination length: {0}", destination.Length.ToString());

Afterwards you can read destination as many times as you like:

// re-set to beginning and convert stream to string
destination.Position = 0;
StreamReader streamReader = new StreamReader(destination);
string text = streamReader.ReadToEnd();
// re-set to beginning and read again
destination.Position = 0;
RssReader cssReader = new RssReader(destination);

(I have seen Endy's comment but since it is an appropriate, current answer, it should have its own answer entry.)