Most vegetable oils, including olive oil, can go rancid. Coconut oil is pretty stable, as are nut oils like almond and walnut. Of course, you have to make sure you don't endanger any guests who may have nut allergies.
The trick I learned from my dad is to seal cutting boards with beeswax and oil. Melt some beeswax in a double boiler or microwave and mix in oil, then rub it into the wood. Put a few layers on. It works great!