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.

Stone Age is a great resource management game on its own, for new players as well as seasoned players alike.

In Stone Age, each player is responsible for developing their tribe, by growing it, feeding it and housing it.  This is a resource management game - meaning you need to decide how to assign your tribe members during the game to accumulate points.

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.

Fluxx is a card game where the rules and victory conditions change throughout the game.  Whilst this can be confusing to people who don't realise that the game is chaotic, it is a lot of fun when you 'get it'.