You forgot to set the width of the border! Change border: red; to border:1px solid red;

Here the full code to get the circle:

.circle {
    background-color:#fff;
    border:1px solid red;    
    height:100px;
    border-radius:50%;
    -moz-border-radius:50%;
    -webkit-border-radius:50%;
    width:100px;
}

<div class="circle"></div>

You are missing the border width and the border style properties in the Border shorthand property :

.circle {
    border: 2px solid red;
    background-color: #FFFFFF;
    height: 100px;
    border-radius:50%;
    width: 100px;
}

<div class="circle"></div>

Also, You can use percentages for the border-radius property so that the value isn't dependent of the circle width/height. That is why I used 50% for border-radius (more info on border-radius in pixels and percent).

Side note : In your example, you didn't specify the border-radius property without vendor prefixes, you propably don't need them as only browsers before chrome 4 safari 4 and Firefox 3.6 use them (see canIuse).

Try this:

.circle {
    height: 20px;
    width: 20px;
    padding: 5px;
    text-align: center; 
    border-radius: 50%;
    display: inline-block;
    color:#fff;
    font-size:1.1em;
    font-weight:600;
    background-color: rgba(0,0,0,0.1);
    border: 1px solid rgba(0,0,0,0.2);
}

.circle {
    border: 1px solid red;
    background-color: #FFFFFF;
    height: 100px;
    -moz-border-radius:75px;
    -webkit-border-radius: 75px;
    width: 100px;
}

Here is a jsfiddle so you can see an example of this working.

HTML code:

<div class="circle"></div>

CSS code:

.circle {
        /*This creates a 1px solid red border around your element(div) */
        border:1px solid red;
        background-color: #FFFFFF;
        height: 100px;
        /* border-radius 50% will make it fully rounded. */
        border-radius: 50%;
        -moz-border-radius:50%;
        -webkit-border-radius: 50%;
        width: 100px;
    }

<div class='circle'></div>