We've never seen this happen to anyone before... at least no one has ever mentioned it nor have I ever seen a post about it on any boards I visit. As long as the switch is done correctly so there is no downtime and you are moving to a host that doesn't have blacklisted IP's you should be fine.
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generally it won't, but you might want to avoid recycled ip's that black clouds hanging over their PR.
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The change of IP *could* have an impact at least in theory if it's a major change.
For example you switch from an American to a European host. Depending on the geographical location your site could be deemed more or less relevant by search engines. With proper planning and a 301 Redirect you should be fine.
Since you are talking about IP address it may be good to have your own, if you share IP with other people whom you don't know (shared hosting) you could be blacklisted just because one of your neighbors has spammed etc
As long as the move over is to a hosting company within the same geographical location and doesn't involve a lot of downtime, it shouldn't hurt your site's search engine rankings.
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