Colonist
A free online version of Settlers of Catan
Fun fact: I briefly worked at Colonist as a PM. But even if I hadn't, this is still my runaway pick to play Settlers of Catan online.
It's very quick to get a game started, but also extremely configurable for advanced players. Expect a standard game to take 30-60 minutes.
Settlers of Catan is a great game, and Colonist is the best web adaptation out there.