Bootstrap 5 (update 2023)
Add some JavaScript to prevent the submenu from closing when the parent dropdown is open. This can be done be toggle display:block...
let dropdowns = document.querySelectorAll('.dropdown-toggle')
dropdowns.forEach((dd)=>{
    dd.addEventListener('click', function (e) {
        var el = this.nextElementSibling
        el.style.display = el.style.display==='block'?'none':'block'
    })
})
Bootstrap 5 Multi-level Dropdown - click
Bootstrap 5 Multi-level Dropdown - hover
Bootstrap 5 Multi-level Dropdown - hover & animate transition
Or, you can use this CSS only method for Navbar dropdowns...
.dropdown-submenu {
  position: relative;
}
.dropdown-submenu .dropdown-menu {
  top: 0;
  left: 100%;
  margin-top: -1px;
}
.navbar-nav li:hover > ul.dropdown-menu {
    display: block;
}
Bootstrap 5 Navbar Dropdown Hover Submenus (CSS only)
Bootstrap 4 (update 2018)
The dropdown-submenu has been removed in Bootstrap 3 RC. In the words of Bootstrap author Mark Otto..
"Submenus just don't have much of a place on the web right now, especially the mobile web. They will be removed with 3.0" - https://github.com/twbs/bootstrap/pull/6342
But, with a little extra CSS you can get the same functionality.
navbar submenu on hover:
.navbar-nav li:hover > ul.dropdown-menu {
    display: block;
}
.dropdown-submenu {
    position:relative;
}
.dropdown-submenu>.dropdown-menu {
    top:0;
    left:100%;
    margin-top:-6px;
}
Navbar submenu dropdown hover
Navbar submenu dropdown hover (right aligned)
Navbar submenu dropdown click (right aligned)
Navbar dropdown hover (no submenu)
Bootstrap 3
Here is an example that uses Bootstrap 3: https://codeply.com/p/T9FWGhhL0S
CSS
.dropdown-submenu {
    position:relative;
}
.dropdown-submenu>.dropdown-menu {
    top:0;
    left:100%;
    margin-top:-6px;
    margin-left:-1px;
    -webkit-border-radius:0 6px 6px 6px;
    -moz-border-radius:0 6px 6px 6px;
    border-radius:0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
    display:block;
}
.dropdown-submenu>a:after {
    display:block;
    content:" ";
    float:right;
    width:0;
    height:0;
    border-color:transparent;
    border-style:solid;
    border-width:5px 0 5px 5px;
    border-left-color:#cccccc;
    margin-top:5px;
    margin-right:-10px;
}
.dropdown-submenu:hover>a:after {
    border-left-color:#ffffff;
}
.dropdown-submenu.pull-left {
    float:none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
    left:-100%;
    margin-left:10px;
    -webkit-border-radius:6px 0 6px 6px;
    -moz-border-radius:6px 0 6px 6px;
    border-radius:6px 0 6px 6px;
}
Sample Markup
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
    <div class="container">
        <div class="navbar-header">
            <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-ex1-collapse">  
                <span class="sr-only">Toggle navigation</span>
                <span class="icon-bar"></span>
                <span class="icon-bar"></span>
                <span class="icon-bar"></span>
            </button>
        </div>
        <div class="collapse navbar-collapse navbar-ex1-collapse">
            <ul class="nav navbar-nav">
                <li class="menu-item dropdown">
                    <a href="#" class="dropdown-toggle" data-toggle="dropdown">Drop Down<b class="caret"></b></a>
                    <ul class="dropdown-menu">
                        <li class="menu-item dropdown dropdown-submenu">
                            <a href="#" class="dropdown-toggle" data-toggle="dropdown">Level 1</a>
                            <ul class="dropdown-menu">
                                <li class="menu-item ">
                                    <a href="#">Link 1</a>
                                </li>
                                <li class="menu-item dropdown dropdown-submenu">
                                    <a href="#" class="dropdown-toggle" data-toggle="dropdown">Level 2</a>
                                    <ul class="dropdown-menu">
                                        <li>
                                            <a href="#">Link 3</a>
                                        </li>
                                    </ul>
                                </li>
                            </ul>
                        </li>
                    </ul>
                </li>
            </ul>
        </div>
    </div>
</div>
P.S. - Example in navbar that adjusts left position: https://codeply.com/p/XEiERVGcmz