Is there any Java API that is like OpenLayers ?
I would like to display google Maps and Openlayers Maps in a java application
Is this what you're after?
http://weblogs.java.net/blog/cajo/archive/2010/10/16/adding-google-maps-your-java-application
You can also use Bing maps with Java, also worth looking at
There's also a useful list of OpenSource Java GIS software here: http://java-source.net/open-source/geospatial
Have a look at GWT-openlayers a GWT wrapper for OpenLayers, or Geomajas a full-blown framework for building GIS web applications.