A good gateway game to the "Euro" style board game. There is a tournament every May long weekend in Edmonton. Other such games include Ticket To Ride, Pirate's Cove and Carcassonne. Settlers is a bit too luck dependent for some - the dice can go cold for you.
http://tripalot.com/games/catan.htm
Beyond that, try Puerto Rico, El Grande, Princes Of Florence, Power Grid, Race For The Galaxy.
There are some great games stores in Calgary - The Sentry Box and Revolution.
http://www.sentrybox.com/
http://www.revolution-games.com/shop/
The top board games as rated at boardgamegeek:
http://www.boardgamegeek.com/browser...=rank&rank=1#1
A new game, Agricola has unseated Puerto Rico as the # 1 game.
Many of these games can be played on-line here:
http://www.brettspielwelt.de/