How can I bind the html <title> content in vuejs?

You can do it with 1 line in the App.vue file, like this:

<script>
    export default {
        name: 'app',
        created () {
            document.title = "Look Ma!";
        }
    }
</script>

Or change the <title> tag content in public/index.html

<!DOCTYPE html>
<html>
  <head>
    <title>Look Ma!</title> <!- ------ Here ->
  </head>
...

There are essentially two ways to solve it.

Use an existing Package

For example, vue-meta:

<template>
  <div id="app">
    <router-view></router-view>
  </div>
</template>

<script>
  export default {
    name: 'App',
    metaInfo: {
      // if no subcomponents specify a metaInfo.title, this title will be used
      title: 'Default Title',
      // all titles will be injected into this template
      titleTemplate: '%s | My Awesome Webapp'
    }
  }
</script>

Create your own Component

Create a vue file containing:

<script>
    export default {
        name: 'vue-title',
        props: ['title'],
        watch: {
            title: {
                immediate: true,
                handler() {
                    document.title = this.title;
                }
            }
        },
        render () {
        },
    }
</script>

Register the component using

import titleComponent from './title.component.vue';
Vue.component('vue-title', titleComponent);

Then you can use it in your templates, e.g.

<vue-title title="Static Title"></vue-title>
<vue-title :title="dynamic.something + ' - Static'"></vue-title>

This answer is for vue 1.x

using requirejs.

define([
  'https://cdn.jsdelivr.net/vue/latest/vue.js'
], function(Vue) {
  var vm = new Vue({
    el: 'html',
    data: {
      hello: 'Hello world'
    }
  });
});
<!DOCTYPE html>
<html id="html">

<head>
  <title>{{ hello }}</title>
  <script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.js" data-main="app"></script>
</head>

<body>
  {{ hello }}
  <input v-model="hello" title="hello" />
</body>

</html>

you can do it like this using the ready function to set the initial value and watch to update when the data changes.

<html>
<head>
<title>Replace Me</title>
</head>
<body>
<script src="https://cdn.jsdelivr.net/vue/latest/vue.js"></script>

<div id="app">
  <input v-model="title">
</div>


<script>
new Vue({
    el: '#app',
    ready: function () {
        document.title = this.title
    },
    data: {
        title: 'My Title'
    },
    watch: {
        title: function (val, old) {
            document.title = val
        }
    }
})
</script>

</body>
</html>

also i tried this based on your original code and it works

<html>
<head>
<title>{{ title }}</title>
</head>
<body>
<script src="https://cdn.jsdelivr.net/vue/latest/vue.js"></script>

<div id="app">
  <input v-model="title">
</div>

<script>
new Vue({
    el: 'html',
    data: {
        title: 'My Title'
    }
})
</script>

</body>
</html>