OK, after looking at celebrities two other types of dreams stood out: those involving animals and mythical creatures. Below you'll see the distribution of the most common animals in dreams reported on twitter. Lots of cats, snakes and fishes!
From my own dreams I definitely remember some involving snakes, but not cats or fishes. Still, animals are powerful symbols in many cultures, for example in Native American or Chinese mythology. There's a also whole bunch of interpretations for dreams involving animals, but I won't go into there now.
Somehow related to animals, but not quite the same are dreams of the next category: mythical creatures. For the first time I tried to use streamgraphs to get an idea of the distribution over time, using Andrew Godwin's graphication library. It's probably not the best possible visualisation for this type of data, but it is visually pleasing.
So: Zombies, Werewolves, Vampires: fight!
Zombies are the undisputed leaders in this category, they occur in a lot of dreams. Are people fearing the Zombie Apocalypse? There definitely is something very modern about the zombie myth, which is more present than older (or old-fashioned?) mythical creatures like vampires and werewolves.
You'll also notice regular spikes in the number reported dreams, which more or less coincide with weekends. People either dream more on weekends, or find more time to tweet about it the next day.
Going back to the zombie apocalypse, another interesting thing I noticed was a short burst of pig/swine related dreams just as it made news end of April this year, visualised in the following graph:
This is a very nice example of how current events (like the swine flu) make their way into the subconsciousness of our minds. It's the zombie pig apocalypse!
Or as pixistyx says on twitter: