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If your intentions are more devious you may benefit from spreading things around, although you might just be fine on the same host. Depends on your level of paranoia and how long you expect them to be around.
On a personal level, I've had link requests from experienced SEO people who won't touch any linked sites on the same IP address.
Whether its fact or fantasy is anyone's guess.... as far as I know there has been no input from those best qualified to provide a definitive answer.
Depends what your intention is. If you sell widgets and wodgets, then there is no problem putting widgets.com and wodgets.com on the same host.
I've had recent experience that suggests being very cautious. I haven't sorted it out completely, but what I think I'm seeing is...
...even if widgets and wodgets use different target terms, if the sites are related in such a way that their inbound links might be coming from related sources, you might have problems.
Eg, if widgets and wodgets were both automotive parts and both sites might be listed in the same directory category, based on what I'm seeing now, I'd definitely recommend different hosts.