Ticket to Ride is an easy to learn board game.

In this game each player takes the role of a train company, aiming to connect cities with your trainline based on cards you collect during the game.  Longer routes offer more points, so that Seattle to Miami would score highly, whilst Boston to New York would have a low score.

Small World is a fun territory claiming game, where players manage different races with special abilities over a number of rounds.  Usually holding more land means more points, however special abilities can also contribute to scoring.