ArcGIS Online servers already have CORS enabled on them but your own ArcGIS Servers or other ones may not. It is a simple process to do this on your own server as described on enable-cors.org. GeoWise has built a useful CORS testing tool which will tell you whether a particular web server already has CORS enabled on it.
Note that Internet Explorer 9 does not support CORS. If your end users are going to be using this browser you will need to get GeoWise to register the map services you want to use with our proxy service.