If the server support what's wikipedia calls byte serving, you can multiplex a file download spawning multiple requests with a specific Range header value (using the AddRange method. See also How to download the data from the server discontinuously？). Most serious HTTP servers do support byte-range.

Here is some sample code that implements a parallel download of a file using byte range:

    public static void ParallelDownloadFile(string uri, string filePath, int chunkSize)
    {
        if (uri == null)
            throw new ArgumentNullException("uri");

        // determine file size first
        long size = GetFileSize(uri);

        using (FileStream file = new FileStream(filePath, FileMode.Create, FileAccess.Write, FileShare.Write))
        {
            file.SetLength(size); // set the length first

            object syncObject = new object(); // synchronize file writes
            Parallel.ForEach(LongRange(0, 1 + size / chunkSize), (start) =>
            {
                HttpWebRequest request = (HttpWebRequest)WebRequest.Create(uri);
                request.AddRange(start * chunkSize, start * chunkSize + chunkSize - 1);
                HttpWebResponse response = (HttpWebResponse)request.GetResponse();

                lock (syncObject)
                {
                    using (Stream stream = response.GetResponseStream())
                    {
                        file.Seek(start * chunkSize, SeekOrigin.Begin);
                        stream.CopyTo(file);
                    }
                }
            });
        }
    }

    public static long GetFileSize(string uri)
    {
        if (uri == null)
            throw new ArgumentNullException("uri");

        HttpWebRequest request = (HttpWebRequest)WebRequest.Create(uri);
        request.Method = "HEAD";
        HttpWebResponse response = (HttpWebResponse)request.GetResponse();
        return response.ContentLength;
    }

    private static IEnumerable<long> LongRange(long start, long count)
    {
        long i = 0;
        while (true)
        {
            if (i >= count)
            {
                yield break;
            }
            yield return start + i;
            i++;
        }
    }

And sample usage:

    private static void TestParallelDownload()
    {
        string uri = "http://localhost/welcome.png";
        string fileName = Path.GetFileName(uri);

        ParallelDownloadFile(uri, fileName, 10000);
    }

PS: I'd be curious to know if it's really more interesting to do this parallel thing rather than to just use WebClient.DownloadFile... Maybe in slow network scenarios?