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If possible, leave your sites up on the old host for a month. Have your DNS entries moved to the new host. Those users & bots querying responsible DNS servers will quickly (probably within a day) be using your new site. Those querying slow-to-update servers (AOL used to be terrible about this) will still go to your old site.
You might consider setting up redirects on your old server IFF you have dedicated IP's for each site on your new server.