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(just my 2-cents)
[edited by: phranque at 10:26 pm (utc) on Mar. 13, 2008]
[edit reason] formatting [/edit]
same ip means same neighborhood and high opportunity for manipulation of backlinks, for example.
another example where ip might be important is click fraud.
One situation involves getting hacked to do parasite hosting - something that has become a significant issue on low cost hosting environments. If a parasite hacker injects a virus onto your pages, then that's a problem both for Google and for your visitors. If the parasite hacker merely injects hidden content (especially links), then that's not so much of a problem for your visitors but is is certainly a problem for Google - without intending it, suddenly your site is breaking Google's guidelines.
There are certainly other hacks in addition to shared ip attacks through cpanel, vdeck and so on,but by eliminating shared IP - at least shared with domains out of your control, you've eliminateed at one concern.
A lot of people like to spread their sites around because of the docID's being stored with the URLs, but the odds are good that Google's onto it so it might not make an awful lot of difference. I'm still paranoid, regardless.
Personally, when using budget hosting it's not only IP that's a concern, I feel if by chance one server has down-time not all the sites go down at once, just some.
I think it was mentioned in a Yahoo thread here a couple of years ago that all the sites on a server got banned, innocent or not, because of being on the same box as some nasties. I don't believe Google would ever go that far, but it's worth keeping in mind.