GeoServer is now able to output maps that look like continuous wrapped maps from Google!
Let’s have a look at an example. Below is a map drawn by GeoServer that is reprojected to a projection that happens to sit across the dateline, the usual “edge” of the map. As you can see the reprojection is not doing a good job where the dateline is crossed:

Polygons crossing dateline change before improving the renderer
However, GeoServer now has what is called advanced projection handling. With this enabled, the dateline wrapping is properly handled and, in addition, the map repeats in a continuous fashion:

Polygons crossing the dateline with advanced projection handling
For more information, including how to turn on this (optional) feature, please see this post from GeoSolutions.