The undecidability of the halting problem yields an easy proof of Gödel's "zeroth" incompleteness theorem:

Statement: Every sound (i.e. not just consistent, but sound) recursive theory of arithmetic is incomplete.

Proof: Assume it is complete. List all its theorems by a program. Then one can decide the halting problem as follows: for any instance, look whether "the program halts" or "the program does not halt" shows up in the list of theorems (since the theory is complete, one of them must show up; and since the theory is sound, the theorem is true).