Q:

How to get list of layers from geoserver

Is it possible to get a list of all the layers served by geoserver? I.e. is there some specific url request to send that does this?

A:

The capabilities links on the geoserver home page each list layers served via various services:

the WMS capabilities lists layers that support requests for tiled images
the WFS capabilities lists layers that support requests for vector data
the WCS capabilities lists layers that support raster queries

A sample WMS request would look like this:
http://demo.opengeo.org/geoserver/wms?request=GetCapabilities&service=WMS&version=1.0.0

A:

So just for completeness, here's an example of how to get a list/array of layers:
        var formatter = new OpenLayers.Format.WMSCapabilities();
        var endpoint = "path/to/wms/endpoint";
        var layers = [];

        // async call to geoserver (I'm using angular)
        $http.get(endpoint + 'request=GetCapabilities').

        success(function(data, status, headers, config) {

            // use the tool to parse the data
            var response = (formatter.read(data));

            // this object contains all the GetCapabilities data
            var capability = response.capability;

            // I want a list of names to use in my queries
            for(var i = 0; i < capability.layers.length; i ++){
                layers.push(capability.layers[i].name);
            }
        }).

        error(function(data, status, headers, config) {
            alert("terrible error logging..");
        });

