One of snippets I use most. I usually include this with every project. Just wrap an embed, iframe or object with a div with a class of embed-container and away you go! You may need to take the height and width off iframe / oject / embed if it happens to be present. For example a Vimeo video embed code usually comes with a height and width on it.

.embed-container {
    position: relative;
    padding-bottom: 56.25%; /* 16/9 ratio */
    padding-top: 30px; /* IE6 workaround*/
    height: 0;
    overflow: hidden;

.embed-container iframe,
.embed-container object,
.embed-container embed {
    position: absolute;
    top: 0;
    left: 0;
    width: 100%;
    height: 100%;