If there are no technical errors, then there's no problems from changes in IP address. You may want to read through the blog post that Matt Cutts made about changing hosting while retaining your same domain name. It's always available through the Hot Topics area [webmasterworld.com], which is always pinned to the top of this forum's index page.

Here's a direct link:
Moving to a New Web Host [mattcutts.com]

I've had a couple of problems with MSN Search when changing hosts/IPs but not the others.

No, it will not affect you unless you move into a bad neighborhood at the new host. But, normally, you won't see any problems at all.

Same domain name, same folder and file names? Should be OK.

as WiseWebDude mentioned one possible issue is the new IP addresses history.

If the new IP address was previously used by a "spammer" or someone else that caused it to be blacklisted, you could have issues. This is very rare, but it does happen (it happened to me about a year ago finally got the "tainted" IP replaced and things reverted to normal).

One other possible issue is the location of the new IP address. Say your site is in Canada and the new IP is located in the US, the change could have a negative affect in your rankings in the ca version of Google (although they've recently added something to the webmaster tools that allows you to choose your preferred location).