A little known trick is that you can use it in Internet Explorer as well using the gradient filter.
background-color: rgba(0, 255, 0, 0.5);
filter: progid:DXImageTransform.Microsoft.Gradient(GradientType=0, StartColorStr='#7F00FF00', EndColorStr='#7F00FF00');
The first hex number defines the alpha value of the color.
Full solution all browsers:
.alpha60 {
/* Fallback for web browsers that doesn't support RGBa */
background: rgb(0, 0, 0) transparent;
/* RGBa with 0.6 opacity */
background: rgba(0, 0, 0, 0.6);
/* For IE 5.5 - 7*/
filter:progid:DXImageTransform.Microsoft.gradient(startColorstr=#99000000, endColorstr=#99000000);
/* For IE 8*/
-ms-filter: "progid:DXImageTransform.Microsoft.gradient(startColorstr=#99000000, endColorstr=#99000000)";
}