I'd like to calculate the distance between a marker and the the very center of the map - can anyone explain how I do this?
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You can use the geometry
library to solve this. You'll need to specify it when loading the Maps JS:
<script type="text/javascript" src="http://maps.googleapis.com/maps/api/js?libraries=geometry&sensor=false"></script>
Then, in your application's code:
var center = map.getCenter();
var markerLatLng = marker.getPosition();
var distance = google.maps.geometry.spherical.computeDistanceBetween(center, markerLatLng);
This returns the distance in meters.

Mike Jeffrey
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The marker is usually set using coordinates, like this: http://code.google.com/apis/maps/documentation/javascript/overlays.html#Markers
And here's a great thread about getting bounds and identifying where the map is centered: Google Map API v3 — set bounds and center
So, now that you have two sets of coordinates, use this formula to calculate the distance: http://www.movable-type.co.uk/scripts/latlong.html