Twitter's typeahead.js suggestions are not styled (have no border, transparent background, etc.)

So looking into the docs I now see:

By default, the dropdown menu created by typeahead.js is going to look ugly and you'll want to style it to ensure it fits into the theme of your web page.

My solution was thus to copy the styling from the example I wished to replicate:

.tt-query, /* UPDATE: newer versions use tt-input instead of tt-query */
.tt-hint {
    width: 396px;
    height: 30px;
    padding: 8px 12px;
    font-size: 24px;
    line-height: 30px;
    border: 2px solid #ccc;
    border-radius: 8px;
    outline: none;
}

.tt-query { /* UPDATE: newer versions use tt-input instead of tt-query */
    box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}

.tt-hint {
    color: #999;
}

.tt-menu { /* UPDATE: newer versions use tt-menu instead of tt-dropdown-menu */
    width: 422px;
    margin-top: 12px;
    padding: 8px 0;
    background-color: #fff;
    border: 1px solid #ccc;
    border: 1px solid rgba(0, 0, 0, 0.2);
    border-radius: 8px;
    box-shadow: 0 5px 10px rgba(0,0,0,.2);
}

.tt-suggestion {
    padding: 3px 20px;
    font-size: 18px;
    line-height: 24px;
}

.tt-suggestion.tt-is-under-cursor { /* UPDATE: newer versions use .tt-suggestion.tt-cursor */
    color: #fff;
    background-color: #0097cf;

}

.tt-suggestion p {
    margin: 0;
}

So, the following styles will give you this look & feel. It's based on the CSS I extracted from the official Typeahead examples website.

CSS:

.tt-query {
  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
     -moz-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
          box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.075);
}

.tt-hint {
  color: #999
}

.tt-menu {    /* used to be tt-dropdown-menu in older versions */
  width: 422px;
  margin-top: 4px;
  padding: 4px 0;
  background-color: #fff;
  border: 1px solid #ccc;
  border: 1px solid rgba(0, 0, 0, 0.2);
  -webkit-border-radius: 4px;
     -moz-border-radius: 4px;
          border-radius: 4px;
  -webkit-box-shadow: 0 5px 10px rgba(0,0,0,.2);
     -moz-box-shadow: 0 5px 10px rgba(0,0,0,.2);
          box-shadow: 0 5px 10px rgba(0,0,0,.2);
}

.tt-suggestion {
  padding: 3px 20px;
  line-height: 24px;
}

.tt-suggestion.tt-cursor,.tt-suggestion:hover {
  color: #fff;
  background-color: #0097cf;

}

.tt-suggestion p {
  margin: 0;
}

This assumes your input will have the form-control class. For my example, it's like this:

<input class="typeahead form-control" type="text" placeholder="States of USA">

https://github.com/bassjobsen/typeahead.js-bootstrap-css/blob/master/typeaheadjs.css

The other ones didn't look great, this one looks most like Bootstrap.