The quickest dependency-less working static-file server. It'll strem files for you.

quickest-static-file-server.js

var http = require('http')
  , url = require('url')
  , path = require('path')
  , fs = require('fs')
  , HTTP_PORT = (process.env.PORT || 3000)
  , server;

server = http.createServer(function (req, res) {
  var publicDir = path.join(__dirname, 'public');
  serveStatic(publicDir, req, res);
});

server.listen(HTTP_PORT, function () {
  console.log('Listening on http://localhost:%d', HTTP_PORT);
});

//----

function serveStatic(rootDir, req, res) {
  var urlPath = decodeURI(url.parse(req.url).pathname)
  getFileStream(rootDir, urlPath, function (err, file) {
    if (err) return handleError(err, res);
    res.writeHead(200, {'Content-Type': file.contentType});
    file.stream.pipe(res);
  });
}

function handleError(err, res) {
  if (err.code === 'ENOENT') {
    res.writeHead(404, {'Content-Type': 'text/plain'});
    res.end('404 BaQa\'! (file not found)');
  } else {
    res.writeHead(500, {'Content-Type': 'text/plain'});
    res.end('500 Ghuy\'cha\'! (something broke)');
  }
}

//----

function getFileStream(rootDir, urlPath, cb) {
  var filepath = path.join(rootDir, urlPath)
  fs.stat(filepath, function (err, stat) {
    if (err) return cb(err);
    if (stat.isDirectory()) return getFileStream(
      rootDir, path.join(urlPath, 'index.html'), cb);
    cb(null, {
        contentType: getContentType(urlPath)
      , stream: fs.createReadStream(filepath)
    })
  });
}

function getContentType(urlPath) {
  return /\.html$/.test(urlPath) ? 'text/html' :
         /\.js$/.test(urlPath) ? 'application/javascript' :
         /\.css$/.test(urlPath) ? 'text/css' :
         /\.ico$/.test(urlPath) ? 'image/x-icon' :
         /\.png$/.test(urlPath) ? 'image/png' :
         /\.jpeg$/.test(urlPath) ? 'image/jpeg' :
         /\.gif$/.test(urlPath) ? 'image/gif' :
         'text/html';
}