My wife and I switched from our old server, Mannoroth, to a newer server, Ravenholdt, that just opened up for transfers a couple of months ago. The process was painless, except for the $25 that my wife had to pony-up, and the $50 I got charged. And the $50 more dollars I will get charged when I need to move my other two alts.
We moved basically because Mannoroth is such an old, established server that it is impossible to find groups for lower level dungeons. I've been on that server since I started playing WoW years ago, but I never spent the amount of times my friends did playing, so I missed out on a lot. I want to experience it with my wife, so we felt the best option was to move to a younger server.
Also, my guild used to be composed of people that I played Counter-Strike with years ago. We had our own gaming severs, since one of us worked for Time Warner and had permission to set up a gaming group. (STNY Gaming) We moved on to Star Wars Galaxies, picked up a bunch of great people, and then hit WoW. After a while, it seemed like all of the people I knew either quit playing completely or just left the STNY guild. So when I had been playing recently, there was nobody left that I used to play with. It was all kids that acted like every other WoW dingus on the planet.
All in all, my wife and I are pretty happy on our new server. The latency is a little higher, but we will deal with it in exchange for running instances when we want to. As a bonus, it's a Role Playing PvP server, so the dingus population is just about half that of a normal PvP server. You see more thoughtful fantasy names and less "Istabsyou" and "Seksyelfchik" names.