The thing I find most interesting about Pangaea is that, if all the landmasses were connected, it leaves a massive amount of uninterrupted ocean everywhere else. It seems to suggest that there is a significant difference between the two areas of Earth; one area being where Pangaea was located, and the other area being the rest of Earth.
Why would only that portion of the Earth be above water? Is there something significant about where Pangaea was located which made it different from the rest of the Earth?
The formation and break up of supercontinents have happened throughout Earth's history in almost a cyclical manner. There may have been many others supercontinents before Pangaea and the total number of such is uncertain. The 4 last supercontinents are: Nuna (some other people call it Columbia) that was present in the period 2.0–1.8 Ga (billion years ago or 1000 million years ago, if you use the long notation); Rodinia that formed around 1.1 Ga and lasted until about 750 Ma; Pannotia that lasted 650-560 Ma; and finally, Pangaea.
The location of the supercontinents seems to have varied throughout Earth's history and it doesn't seem likely that there was something special about the location of Pangaea, except the underlying forces of plate tectonics.
Here is good animation of the evolution in time of the different supercontinents.
Just to add, cause I don't see it in the answers above. Continents are no heavier than oceans. As far as the Earth is concerned, they weigh about the same and they drift according to the flow of the mantle underneath.
Like marshmallows in cocoa, sometimes they will drift and touch (and by touch, I mean, crash into each other and form Himalaya sized mountain ranges) and sometimes they will float apart. There's nothing strange about the continents all being together.