I think (without having played Settlers) that in an ideal board game you shouldn't be able to get into a position where you know you're going to lose until the very end of the game. That's a big problem with Monopoly -- it's too easy to die a slow and painful death as you mortgage and sell your properties one by one. The further you are behind, the harder it is to get ahead.

This is why I like skill-based yet luck-dependent games like Scrabble or Trivial Pursuit. Even if you're 150 points behind in Scrabble, there's always the chance you're going to get two great racks in a row. And even if you're six pie-slices behind in Trivial Pursuit there's always the chance that you'll get a long run of questions you happen to know the answers to.

Risk and Monopoly take so long to finish that player elimination is a necessity. Games of Settlers where one player has no hope of winning aren't common, as long as players are of relatively equal skill.