I've moved several websites to different hosts, and while I have never received a negative effect on my rankings, the amount of time it took to index posts increased. For example, before I moved, the posts would be crawled and indexed within 1 minute of posting (several year old website.) After moving however, the posts would take upwards of 24 hours. This was only temporary though, as after a little while the indexing rate returned to normal.
Regards,
~ver.