Not elegant, but should work

target.innerHTML = target.innerHTML.replace(/\n|\t/g, ' ');

In the below example all new lines \r\n or spaces between HTML tags are removed, and on the second phase the content within HTML tags is minified, so extra spaces are eliminated.

Finally trim() is used to remove spaces before & after the final resulting string.

// dummy string to minify
var s = `

    <div   value="a"     class="a b"   id="a">
      <div>
        foo   bar  
        <br><br>
        <span>baz</span>   <i>a</i>  
      </div>
    </div>
`

function minify( s ){
  return s
    .replace(/\>[\r\n ]+\</g, "><")
    .replace(/(<.*?>)|\s+/g, (m, $1) => $1 ? $1 : ' ')
    .trim()
}

console.log(  minify(s)  )

The above is also available as a gist in my collection

Edit 2 (Feb 22, 2017): Now the best tool to minify your assets (and a whole lot more, by adding loaders and plugins) is definitely Webpack.

Example of config to move all your .css in one file and minify it:

{
  test: /\.css$/,
  use: [
    {
      loader: 'css-loader',
      options: {
        minimize: true
      }
    }
  ]
}

Edit 1 (Sept 16, 2014): Even better, now you have task runners like Gulp or Grunt.

Task runners are small applications that are used to automate many of the time consuming, boring (but very important) tasks that you have to do while developing a project. These include tasks such as running tests, concatenating files, minification, and CSS preprocessing. By simply creating a task file, you can instruct the task runner to automatically take care of just about any development task you can think of as you make changes to your files. It’s a very simple idea that will save you a lot of time and allow you to stay focused on development.

Must read: Getting started with Gulp.js

Example of task with JavaScript concatenation and minification (and JSHint):

gulp.task('scripts', function() {
  return gulp.src('src/scripts/**/*.js')
    .pipe(jshint('.jshintrc'))
    .pipe(jshint.reporter('default'))
    .pipe(concat('main.js'))
    .pipe(gulp.dest('dist/assets/js'))
    .pipe(rename({suffix: '.min'}))
    .pipe(uglify())
    .pipe(gulp.dest('dist/assets/js'))
    .pipe(notify({ message: 'Scripts task complete' }));
});

Original answer (Jul 19, 2012): I advise the HTML5 Boilerplate Build Script which can minify your JS and CSS.