My favorite one is chess games. If you managed to compress each chess game down to just a single atom, the physical size of a disk to save this data would exceed the amount of atoms in the universe. Even the number of theoretic positions (ignoring legality/possibility) is just below the number of atoms in the universe.
replyThough it must be said that once one starts looking at permutations of things, the number of atoms in the universe seems quite small indeed. 10^80? What's that, like 7 or 8?
The number of permutations of n distinct objects is n!. So, probably a bit more than 8, since 8! < 10⁸, but I don’t think you are terribly off :-)
replyEdit: 58! < 10⁸⁰ < 59!