Nov 26th 2010 9:43AM I have moved realm twice.
The first time my friends and I were just fed up with the realm itself (someone had just stolen the guild bank) and we decided to move to an RP-PvP realm hoping the RP tag would keep away the more immature players. There were five of us so we levelled together and had a great group composition for five man dungeons, it was a lot of fun. However, once we got to max level (70 at the time) we started realising that the raid progression on the realm was awful mostly due to the low population of the realm. Despite having made friends there we eventually decided to leave in an attempt to get into a more competent raiding guild.
This time we were smarter, we researched the realm, rolled low level characters first and talked with the people there who were raiding. Eventually we transferred our mains or levelled brand new mains, we even managed to convince some of our friends to come with us and now we are much happier.
My advice to anyone choosing a new realm is to not only research it but ask the people on that realm about it in game (I wouldn't really trust the wow forums for this).