You can play settlers (or the cities&knights expansion) at games.asobrain.com
It's free.
Due to copyright (I guess) they've named the games something different, but the rules are exactly the same as the board games.
Settlers -> Xplorers
You can also play carcasonne (another 'gateway' game like settlers, a popular choice for people new to decent modern board games) on that site, where it is called Toulouse.
Once you've got going with settlers, there are loads of other good board games you can try. You can find details on hundreds of them at:
www.boardgamegeek.comI personally find that "Puerto Rico" and "Race for the Galaxy", which are somewhat similar in gameplay, are both absolutely excellent games and are distinctly better than Settlers of Catan. Those two get requested more than any others when playing board games with my friends.