AFnord: I've found that to largely depend on the game. I've had no problems with getting people to sit down and play a long game of Arkham Horror, but would be unable to get them to stick around for a whole game of Monopoly or "Nya Finans" (a semi-local Monopoly-like game). They key to finding a game that works even if it is a bit on the long side, is to find one that engages the players.
Alfie3000: I've never ventured past the classic mainstream boardgames (Monopoly, Cluedo, Snakes & Ladders). I'd be interested in something like Risk or Axis & Allies but I guess they suffer from the same players being eliminated as Monopoly. What would you suggest as good board game that keeps players in and engaged ?
I used to like Monopoly, until I got introduced to the games outside of the classics.
Axis is a bit better in this regard, but I still don't find it to be ideal. The above mentioned
Arkham Horror though, it is really good, and has the added advantage of it being enough for one player to know all the rules (it is a co-op game, players vs the game, and only one player needs to know how to handle all the non-player mechanics).
I also mentioned
Cosmic Encounter earlier in this thread. It is a game with a lot of replay value, as you randomize which race each player plays, and there are a lot of them, all of which play very differently. The core rules are really easy though.
Agricola is a relatively new game, that quickly became one of the most popular Eurogames around. Rules are a bit more complex than the average Eurogame, but it is still a game that is easy to get into, and yet has a good amount of depth to it.
Race for the Galaxy is an interesting game, about building a galactic empire. It might look intimidating, with all those strange symbols, but it is actually a really easy game to play.
And here are some other easy to get into "must play" games in no particular order:
Settlers of Catan,
Space Hulk,
Carcassone And visiting Boardgame geek always reminds me of all the games I need to pick up at one point or another...
Generally speaking, I would actually recommend against playing boardgames from the 80's or prior. Much like video games, boardgames do actually age, with new and sleeker mechanics replacing the old. And much like video games, there are plenty of notable exceptions, but in general, BGs have evolved a lot.