If I were to improve my board game collection, which board games would I add?

Over the past year or so, I’ve taken up a greater interest in board games. I don’t own much of a collection of games, however, as I play with my friends using their copies of games.

I want to find board games that are more in-depth than the “mass-market” games (Monopoly, Clue, etc.) but that are still appealing to a wider audience.

In terms of game complexity/depth, the most complicated game I’ve ever played is Twilight Imperium III, which is pretty massive. My family sticks to games such as Clue or Trivial Pursuit.

What board games would you recommend?