'Settler's of Catan' is a great game to begin with, and needs 3
players to play - but comes only with 4 player capability. This
lets the game expand - and the gameboard expand - to 5 or 6
players. The game certainly takes longer with more players, but is
very enjoyable for the jump in complexity. Also, having more room
allows more space for the game to grow (on the original board,
there are times where there's nowhere to go, if people place their
original settlements too close to each other).
You require the original board game to make any use of this game.
Adding in Cities and Knights or Seafarers is another way to make
the game all the larger and complex; and both can also be expanded
to 5 or 6 players.