I've been doing some software development for someone, and part of the exercise involved me connecting to one of his servers in order to try out the software. One day he told me he was moving out of his office in order to go somewhere with more space, and that the system would be down for a few days while he moved.
Once he'd moved, I asked what his new IP address range was. "Oh, it's the same as before", came the reply.
Y'know, it never occurred to me that your IP addresses could be made to follow you. Of course, it makes perfect sense that you should be able to do it like this - it was just a bit of failing to spot the blatantly obvious on my part.
Worth bearing in mind for anyone who's about to move office, that.