I just changed IP addresses for about 20 clients and was worried there might be some problems with SERPs but everything went smoothly. The important thing is to make sure your site is up on the old server for a few days at the same time it is on the new server just in case the friendly spider comes to the wrong address.
I have recently gone through the same process and was worried it may affect some sites we transferred. Although it now seems to have gone fine and SERPS are fully restored we did notice a drop in SERPs for a few weeks after the transfer.
I put out a request to other SEO friends prior to the transfer and it seems this is quite normal so don't panic if you do take a drop in SERPs!