I've heard that linking to a site from the same server is bad for SEO. If the link is set to rel no-follow, would that be OK?
It's not bad and it doesn't hurt you. IPs are scarce and IPv6 isn't standard yet. Your search rankings don't go down because of links from the same IP. No-one knows, other than Google, how they calculate the value of a link coming from the same IP. Is it the same domain or just same server with IP? Is it coming from a related page, an authority domain etc? There are so many variables and no-one knows, other than Google, how they affect your rankings, but they surely do not harm your rankings.
Except that doesn't make sense at all. We were just discussing this same thing at my office, because I have a personal blog hosted on the same server (under a different account).
I don't think it matters because that would mean that every blogger who is in a shared server (á la 1and1, godaddy or whatever) would be penalized when linking to each other.
Linking to the website from the same server with same IP address is bad. As per my knowledge if you can have multiple static-ip assigned to your websites that should be okay.
Basically linking internally should not create a negative impact, it should just not be that positive. Because if you see google takes it positive if a blog is having interlinked posts. So same way it should have less positive impact rather than negative impact.
I would suggest you should have it as friend or sister link rather than nofollow so that google knows that these website belongs to same network.
My experience is that linking from sites on the same server does get a penalty, I have tried this and my site suffered and as soon as I removed the links my site recovered. If you think about it, it is cheating really. A link is supposed to be a vote of confidence from someone unrelated to you or your site ie a different server usually in a different location. Sticking a domain on your own server then voting for yourself is cheating.
The same server alone won't matter. You could technically have someone you don't know or a friend on a same server and that doesn't necessarily mean it's cheating. There is a chance that your friend could genuinely think you have great content.
However, if you have both domains registered to the same name and you have both domains on the same server, I'm going to go out on a limb and say that would get a penalty. Eventually. It might take a manual spam action after some investigating for that penalty to happen.