I've made some minor changes to your code. In fact I've added a few properties to your layer:

    isBaseLayer: true, 
    wrapDateLine: true, maxExtent: 
    new OpenLayers.Bounds(-180, -180, 180, 120)

And here's the whole code for you, to easily test it. Just zoom out and move the map, as you like.

<!DOCTYPE HTML>
<html>
  <head>
    <title>skobbler tiles with OpenLayers Demo</title>
	<base href="http://tiles1.api.skobbler.net/tiles/" />
	<script src="http://storage.api.skobbler.net/web/js/openlayers/openlayers-2.12/OpenLayers.js"></script>
	<script>
		
		function init() {
		
		    var options = { 
                  };

			map = new OpenLayers.Map('map');
					
			var skoLayer = new OpenLayers.Layer.XYZ("skobbler",
				["${z}/${x}/${y}.png?api_key=23e8c5a8821c771a301201fcb5556771", 
			     "${z}/${x}/${y}.png?api_key=23e8c5a8821c771a301201fcb5556771",   
			     "${z}/${x}/${y}.png?api_key=23e8c5a8821c771a301201fcb5556771",
			     "${z}/${x}/${y}.png?api_key=23e8c5a8821c771a301201fcb5556771"], 
			{numZoomLevels: 18, sphericalMercator: true, isBaseLayer: true, 
			wrapDateLine: true, maxExtent: new OpenLayers.Bounds(-180, -180, 180, 120),
			attribution: 'Map data &copy; <a href="http://www.openstreetmap.org" target="_blank">OpenStreetMap</a> contributors, <a href="http://www.openstreetmap.org/copyright" target="_blank">Terms</a>, Tiles courtesy of <a href="http://www.skobbler.com" target="_blank">skobbler</a>'});
		map.addLayer(skoLayer);
        map.setCenter(
                new OpenLayers.LonLat(10.546875,51.17934297928927).transform(
                    new OpenLayers.Projection("EPSG:4326"),
                    map.getProjectionObject()
                ),4
            );
      }
    </script>
  </head>
  <body onload="init();">
    <div id="map" style='width: 500px;height: 500px;'></div>
  </body>
</html>