Aside from the blindingly obvious (Build the Great Wall, check to see if you left "Raging barbarians" on, turn barbarians off, BUILD MORE UNITS, etc), there are a few things you can do here:
1: Make sure your cultural borders extend over a vast swath of terrain- Barbarians won't spawn within your cultural borders, nor will they spawn within any tile that you have line of sight to.
2: Try to connect all your cities with roads and have several high mobility units (Horse Archers, Chariots, etc) on stand-by in or near your cities which are closest to unoccupied areas.
3: Scatter units around areas that belong to neither you nor the computer, so that you constantly have line of sight in all the areas where barbarians could spawn. This gets less and less practical on bigger maps, but at the very least it can provide you with advance warning of approaching enemies.
-edit-
Go to custom game instead of start a new game.