How to display mouse position as tooltip in OpenLayers-2?

you can convert pixels to lat/long with the help of getLonLatFromPixel() function.

See also openlayers FAQ.

To add to simo's answer... here's an example:

map.events.register("mousemove", map, function (e) {
    var position = e.map.getLonLatFromViewPortPx(e.xy);
    OpenLayers.Util.getElement("tooltip").innerHTML = "<label>Latitude: " + position.lat + "</label><br/><label>Longitude: " + position.lon + "</label>";
});

You may need to transform from Mercator to Geographic as i did... if so:

var position = e.map.getLonLatFromViewPortPx(e.xy).transform(new OpenLayers.Projection("EPSG:900913"), new OpenLayers.Projection("EPSG:4326"));

As of Openlayers 2.12 the following approach works for accessing the coordinates from hovering:

map.events.register("mousemove", map, function (e) {            
var point = map.getLonLatFromPixel( this.events.getMousePosition(e) )     
    console.log(point.lon, point.lat)
});