JSactions.htm

<apex:page controller="apexController">
    <script>
        window.onload = function()
        {
            var formElement = document.querySelector("[id$='pageForm']");
            if(formElement.addEventListener)
                formElement.addEventListener("keypress", function(e)
                {
                    if(e.keyCode === 13)
                    {
                        // do stuff
                        SearchJS();
                        e.preventDefault();
                    }
                }, false);
            else if(formElement.attachEvent)
                formElement.attachEvent("onkeypress", function(e)
                {
                    if(e.keyCode === 13)
                    {
                        // do stuff
                        SearchJS();
                        return e.returnValue = false;
                    }
                });
        }
    </script>

    <apex:form id="pageForm">
        <apex:actionFunction action="{!doSearch}" name="SearchJS" reRender="resultTable, ErrorPanel" status="SearchingStatus" />
        <!-- Rest of the form -->
    </apex:form>
</apex:page>