About 4 years ago we moved our hosting. As described in earlier posts, everything was replicated onto our new server beforehand, until all that remained was to switch the nameservers.
This was done, and there was no interruption or impact on our rankings. Everything was fine, and there really was no need to panic.
I guess the rule is, make sure the groundwork is done thoroughly and properly and then switch... you shouldn't have a problem.
Regards,
Chris