Ticket to Ride and Settlers of Catan are great. I play them single player though, so while they both have multiplayer, I can't comment on the strength of their community.
A lot of them! Tanto Cuore and Ascension are my favorite. You should definitely have a look at Playdek games. Moreover there are lots of other boardgames ported to ios although there are not so many online players as in Playdek games.