My friends and I regularly get together for game nights. We have a dozen different games from Monopoly to Puerto Rico, but as often as not we end up playing Settlers of Catan. There is something about this game. It can be explained in minutes and is accessible to nearly anyone. I have seen a 7 year old play the game and do well(although we no longer allow him to trade with his father) as well as people who have never played a game more complex than monopoly or life.
The typical game of Catan takes less than an hour, a bit more with more people but not much because every turn can bring resources to every player. The basic game mechanic is rolling two six sided dice and then gathering resources from anyplace that has that number which borders your settlements. You then use those resources to build settlements, roads and cities so you can gain more resources. The brilliance of the game is in trying to decide which of those things to do. Do you buy the city in the location you're already at or spread to another before you opponent can get there. Should you work towards having the largest army, or are you better off building roads? Can you afford to save the resources when you could lose half of them when someone rolls a 7?
The game has numerous expansions, but those hardly seem necessary because even with the seeming simplicity of the game we are able to play enough variations that it doesn't get old. Sometimes the map gets laid out so that the resources are even, other times they are randomly put out so you may end up with most of the forests in one part of the game, and the numbers put on those are almost always random and hidden until after you have bulit next to it, meaning that putting your piece in the center of three resources you really want may be great, or it may mean that you end up with three numbers that almost never get rolled.
We have even found that if you go to 15 points you can play a reasonible 2 person game of Settelers of Catan though that almost completly leaves out trading. It is very difficult to get someone to trade with you when they are your only opponent and you want to build a road to cut them off from part of the board.
Other people almost certainly play the game differently and that is part of the fun of Catan. It has found the sweet spot between so simple that there are no rules which can be changed to alter the feel of the game and so complex that every minor change risks bringing ruin into the game. I will continue to explore new games, but when I want to sit back, relax and play a game that I know I will enjoy every time it is almost certainly gong to be Settlers of Catan.