With mods it's possible, @izagor knows all about that.
Without mods it's only possible when you put all family members in one household (8 max, don't forget putting the urns of dead relatives into the inventory) and save them to the bin. Open the new world and put your family in. When there are sims with a rabbithole career like fireman or film director don't forget to put in that rabbithole into the world first. Otherwise the sim won't have a job anymore.
Once the family is in the world you can move everyone to other houses.
There is no connection possible with other worlds without mods (except the WA worlds, the campus and Oasis Springs of course).
