See this similar question:
Google Maps V3: Draw German State Polygons?
The Natural Earth Data Set in FusionTables has country polygons available in it. You can style them as you like.
I used it to create this example:
http://www.geocodezip.com/v3_FusionTablesLayer_worldmap_linkto.html
Here is an example that uses a KmlLayer:
http://www.geocodezip.com/v3_GoogleEx_layer-kml_world_countries_simple.html
code snippet:
var kmlLayer = null;
var map = null;
function openIW(layerEvt) {
if (layerEvt.row) {
var content = layerEvt.row['admin'].value;
} else if (layerEvt.featureData) {
var content = layerEvt.featureData.name;
}
document.getElementById('info').innerHTML = "you clicked on:<br>" + content;
}
function initialize() {
var chicago = new google.maps.LatLng(36.4278, -15.9);
var myOptions = {
zoom: 0,
center: chicago,
mapTypeId: google.maps.MapTypeId.ROADMAP
}
map = new google.maps.Map(document.getElementById("map_canvas"), myOptions);
google.maps.event.addListener(map, "click", function() {
document.getElementById('info').innerHTML = "";
});
kmlLayer = new google.maps.KmlLayer('http://www.geocodezip.com/geoxml3_test/world_countries_kml.xml', {
preserveViewport: true,
suppressInfoWindows: true
});
kmlLayer.setMap(map);
google.maps.event.addListener(kmlLayer, 'click', openIW);
}
google.maps.event.addDomListener(window, 'load', initialize);
<script src="https://maps.googleapis.com/maps/api/js?key=AIzaSyCkUOdZ5y7hMm0yrcCQoCvLwzdM6M8s5qk"></script>
<table>
<tr>
<td>
<div id="map_canvas" style="height:200px; width:300px;"></div>
</td>
<td>
<div id="info"></div>
</td>
</tr>
</table>