The spaces are not the problem ... I tried it with your url and it's working
try {
    String urlString = "http://www.hospimedica.com/images/stories/articles/article_images/_CC/20110328 - DJB146.gif";
    URL url = new URL(urlString.replaceAll(" ", "%20"));
    URLConnection connection = url.openConnection();
    connection.setRequestProperty("User-agent", "Mozilla/4.0");
    connection.connect();
    InputStream input = connection.getInputStream();
    Log.d("#####", "result: " + BitmapFactory.decodeStream(input));
} catch (MalformedURLException e) {
    e.printStackTrace();
} catch (IOException e) {
    e.printStackTrace();
}
The important line is connection.setRequestProperty("User-agent", "Mozilla/4.0");
I don't know why that solves it, but it has obviously worked before here.