I suspect Basil is at least in the running, everyone I know who starts growing Basil at home ends up cloning it endlessly and gifting them for lack of space. Aloe is another I've seen follow a similar pattern.
Mint is pretty resilient too, I accidentally left a (large) pot of it on the balcony over the winter in Helsinki. It spent a couple of months at -10, and was covered in ice/snow too.
When some came around again in March this year it was still alive, much to my surprise.