Are any genes over a billion years old?
Ribosomal RNA (rRNA) genes are shared among all living organisms, including lineages that have diverged from one-another well before a billion years. Bacteria, Archaea, and Eukaryotes diverged over 3 billion years ago, and their rRNAs are virtually identical to one-another. http://www.biologyreference.com/Ar-Bi/Archaea.html
Any genes that are shared between plants, animals and fungi would also be over a billion years old.