My favourite is traditional Genoese style.
But I have been experimenting recently with a red "pesto" that you can make from the vegetable counter in winter, involving sweet red peppers, sun dried tomatos, garlic, olive oil, parmesan and pecorino, pine nuts, and just a few fresh basil leaves if you have them (otherwise I think that good dried would do here).
So far it has been very successful. I will post it when I have it perfected.
Thanks to bang bang for giving me the idea.