Twenty Twelve is the 2012 official theme for Wordpress. I like having a transparent background for all my posts and pages. To do so, edit the stylesheet (style.css) of the theme and replace

/* Page structure */
.site {
    padding: 0 24px;
    padding: 0 1.714285714rem;
    background-color: #fff;
}

by

/* Page structure */
.site {
    padding: 0 24px;
    padding: 0 1.714285714rem;
    /* background-color: #fff; */
    background-color: transparent;
}

This change will be erased at the next update of Twenty Twelve theme. A best practice would be to derive a child theme and only modify this one...