[Vuejs]-Vue Element not being rendered

No need to register your component twice. Remove components section and simply add Vue.component before the instance. Like this

Try this

app.js

Vue.component('example', require('./components/Example.vue'));

Vue.component('navigation', require ('./views/navigation.vue'));

const app = new Vue({
    el: '#app'
});

views/navigation.vue

<template>
    <nav class="navbar navbar-inverse navbar-fixed-top">
        <div class="container">
            <div class="navbar-header">
                <button type="button" 
                        class="navbar-toggle collapsed" 
                        data-toggle="collapse" 
                        data-target="#navbar" 
                        aria-expanded="false" 
                        aria-controls="navbar"
                >
                    <span class="sr-only">Toggle navigation</span>
                    <span class="icon-bar"></span>
                    <span class="icon-bar"></span>
                    <span class="icon-bar"></span>
                </button>
                <a class="navbar-brand" href="#">Project name</a>
            </div>
            <div id="navbar" class="collapse navbar-collapse">
                <ul class="nav navbar-nav">
                    <li class="active"><a href="#">Home</a></li>
                    <li><a href="#about">About</a></li>
                    <li><a href="#contact">Contact</a></li>
                </ul>
            </div><!--/.nav-collapse -->
        </div>
    </nav>
</template>

<script>
    export default {
        mounted() {
            console.log('Component mounted.')
        }
    }
</script>