Playing a game with the intention of skipping agriculture is not wise, what if you have lots of farm resources in your area? It's pretty much a given that at some point you'll need agriculture or animal husbandry, because farm / animal resources will exist in your area. The need for these depends on the map.
That being said, if I don't start with mysticism, I've played games where I don't research it for a long time, like until 1 AD. That seems to be the only one you could optionally skip. Maybe fishing too, if it's a pangaea map. But then again, calendar resources often abound, so fishing eventually becomes necessary.