It actually should be a colon rather than a semicolon, when a list follows it: "I'd like to thank my parents: Oprah Winfrey and God." (The colon always introduces either a list, or something that's being introduced as a direct follow-on from the statement before it — like, well, how I used it in the previous sentence.)
It's a bit complicated to explain, but it's set out pretty well in one of my favourite books on this topic, the legendary
Eats, Shoots and Leaves by Lynne Truss. I'm away from home at the moment, though, so unfortunately (or maybe fortunately) I can't quote from it!!