To build upon @6twenty's answer...I prefer panTo(LatLng) over setCenter(LatLng) as panTo animates for smoother transition to center "if the change is less than both the width and height of the map". https://developers.google.com/maps/documentation/javascript/reference#Map
The below uses Google Maps API v3.
var marker = new google.maps.Marker({
position: new google.maps.LatLng(latitude, longitude),
title: markerTitle,
map: map,
});
google.maps.event.addListener(marker, 'click', function () {
map.panTo(marker.getPosition());
//map.setCenter(marker.getPosition()); // sets center without animation
});