My business is... troublesome.
What I do is legal in every country on earth, but some people don't like it, and make it so tough on my poor ISPs that I am forced to go looking for new providers more often than I would like.
The only option I know of for somebody in my position is called "bulletproof hosting" (think wikileaks) and it isn't cheap.
The only thing that makes bulletproof hosting expensive, or anything different than typical hosting, is their legal stance when responding to "abuse" complaints via email. Your typical host will get fed-up after 5 or 10 no matter what the reason, and a bulletproof host will take the time to look through the legality of the matter and make a decision based on that.
As far as I know, these abuse emails are directly tied to the ip address on which their server sits, because they "own" that ip address and have the ability to lease it out to me on my expensive bulletproof server.
If I could answer them personally, I would save another company the trouble and hopefully save myself some money along the way.
How can I become the bulletproof host? Just rent out a room in my local DC and ask where to get the IPs from?
P.S. No... just because I know this will be the first question everyone asks - I am not some spammer or rule 34 pornographer, what I do is legal in every country. I said "think wikileaks"!
EDIT: Thank you once again for all of the amazing responses. Don't know why I've been lighting fires here recently. Thanks to everyone who saw through the smoke and provided me with meaningful answers.