Bootstrap 5: (Same as v4x)
<div class="progress position-relative">
    <div class="progress-bar" role="progressbar" style="width: 60%" aria-valuenow="60" aria-valuemin="0" aria-valuemax="100"></div>
    <small class="justify-content-center d-flex position-absolute w-100">60% complete</small>
</div>
Bootstrap 4 with utility classes: (Thanks to MaPePeR for the addition)
<div class="progress position-relative">
    <div class="progress-bar" role="progressbar" style="width: 60%" aria-valuenow="60" aria-valuemin="0" aria-valuemax="100"></div>
    <small class="justify-content-center d-flex position-absolute w-100">60% complete</small>
</div>
Bootstrap 3:
Bootstrap now supports text within a span element in the Progress bar. HTML as provided in Bootstrap's example. (Notice the class sr-onlyis removed)
HTML:
<div class="progress">
    <div class="progress-bar" role="progressbar" aria-valuenow="60" aria-valuemin="0" aria-valuemax="100" style="width: 60%;">
        <span>60% Complete</span>
    </div>
</div>
... It does however only center the text according to the bar itself, so we need a little bit of custom CSS.
Paste this in another stylesheet/below where you load bootstrap's css:
CSS:
/**
 * Progress bars with centered text
 */
.progress {
    position: relative;
}
.progress span {
    position: absolute;
    display: block;
    width: 100%;
    color: black;
 }
JsBin file: http://jsbin.com/IBOwEPog/1/edit
Bootstrap 2:
Paste this in another stylesheet/below where you load Bootstrap's CSS:
/**
 * Progress bars with centered text
 */
.progress {
    position: relative;
}
.progress .bar {
    z-index: 1;
    position: absolute;
}
.progress span {
    position: absolute;
    top: 0;
    z-index: 2;
    color: black; /* Change according to needs */
    text-align: center;
    width: 100%;
}
Then add text to a progress bar by adding a span element outside .bar:
<div class="progress">
    <div class="bar" style="width: 50%"></div>
    <span>Add your text here</span>
</div>
JsBin: http://jsbin.com/apufux/2/edit