I am using world imagery online and i have a internet speed of 10Mbps,but image is taking too much of time to open in arcmap 10.2 and same is the problem when i zoom in the base maps especially on the conic and polar projection systems@
Another thing I forgot to mention in my previous post is check the location of your local cache folder. ArcGIS will store cached tiles into your My Documents folder. In most cases it will be a local folder i.e in Windows 7 you can find it under the folder
C:\Users\<UserName>\AppData\Roaming\ESRI\Local Caches
However if your IT department has sent your My Documents folder to a folder on the network, it can impact your local cache performance. If it's not on your Local, try changing. See here ArcGIS Help 10.1
As another option try clearing the Local Caches folder, let Arc rebuild your cache and see if that helps. I've never had success with that but I have heard of others that have had success with it
Thanks.
Support services blog named "Troubleshooting issues adding ArcGIS Online basemaps to ArcMap" can be found here.