Center content in responsive bootstrap navbar

I think this is what you are looking for. You need to remove the float: left from the inner nav to center it and make it a inline-block.

.navbar .navbar-nav {
  display: inline-block;
  float: none;
  vertical-align: top;
}

.navbar .navbar-collapse {
  text-align: center;
}

http://jsfiddle.net/bdd9U/2/

Edit: if you only want this effect to happen when the nav isn't collapsed surround it in the appropriate media query.

@media (min-width: 768px) {
    .navbar .navbar-nav {
        display: inline-block;
        float: none;
        vertical-align: top;
    }

    .navbar .navbar-collapse {
        text-align: center;
    }
}

http://jsfiddle.net/bdd9U/3/

The original post was asking how to center the collapsed navbar. To center elements on the normal navbar, try this:

.navbar-nav {
    float:none;
    margin:0 auto;
    display: block;
    text-align: center;
}

.navbar-nav > li {
    display: inline-block;
    float:none;
}