Building on BalusC's answer I came up with the following (tested on IE and FireFox):
<h:form id="form" onkeypress="ifEnterClick(event, #{rich:element('searchButton')});">
where ifEnterClick is defined by:
/**
 * Handler for onkeypress that clicks {@code targetElement} if the
 * enter key is pressed.
 */
function ifEnterClick(event, targetElement) {
    event = event || window.event;
    if (event.keyCode == 13) {
        // normalize event target, so it looks the same for all browsers
        if (!event.target) {
            event.target = event.srcElement;
        }
        // don't do anything if the element handles the enter key on its own
        if (event.target.nodeName == 'A') {
            return;
        }
        if (event.target.nodeName == 'INPUT') {
            if (event.target.type == 'button' || event.target.type == 'submit') {
                if (strEndsWith(event.target.id, 'focusKeeper')) {
                    // inside some Richfaces component such as rich:listShuttle
                } else {
                    return;
                }
            }
        }
        if (event.target.nodeName =='TEXTAREA') {
            return;
        }
        // swallow event
        if (event.preventDefault) {
            // Firefox
            event.stopPropagation();
            event.preventDefault();
        } else {
            // IE
            event.cancelBubble = true;
            event.returnValue = false;
        }
        targetElement.click();
    }
}
Edit: Since selecting a value from Firefox form auto completion using the enter key fires a keydown event, but no keypress event, using onkeypress is preferable to onkeydown.