It's definitely cool to think about how a 2D universe might be organized and how it might operate. I haven't read Planiverse, but I understand that it imaginatively examines how confining a universe like ours into a 2D universe would affect evolution and the order of things. So, we know that our universe is 3D, and we don't know about anything real that is separate from or outside of the universe around us that we have studied, so I would say that we can't observe or visit a real universe that is 2D.

However, we can observe certain systems (not the entire universe) that are 2D, for example, molecular systems like graphene that have special physical properties because of their 2D nature. We can use mathematical constraints or computer simulations to restrict traditionally 3D systems to 2D systems to see how the physics changes under these constraints. However, just because we can look at things mathematically or with simulations doesn't necessary give them physical reality.

We don't have any evidence right now that a 2D universe would be possible (say if the universe collapsed and re-expanded but only in 2 dimensions), but it sure is interesting to think about that scenario and what it would mean--if such a system could ever support life, whether planets could ever form, whether stars could form, and what there would be in place of these familiar objects in a universe so vastly different from the one in which we live.

A two-dimensional space does not describe the physics of our universe. We have no means of observing any universes apart from our own, and therefore do not know if they exist or not; consequently, whether or not there are or can be universes that do is not something that science can answer, except possibly by modelling them (e.g. using computers, which we already do). We currently do not know of the existence of other universes, and as a result have no known ways of visiting them.