I bought this game for my brother's birthday just because it was a spiel des jahres winner. But we just left in the box for a while and didn't finally play it until the town got blasted with a snowstorm and there was nothing to do. We had no idea how to play the game at first, and it took a few games before any kind of strategies emerged. But then someone did some chaining with the villiage and we started to understand the concept of "building an engine". Got addicted to the game quickly after that! Love the whole series. My favorite game, for sure!
I love Ticket to Ride! It is one of my "go to" games when wanting to play a board game with people that haven't played before. The rules are easy to learn, and all players in the game can feel like they are making progress towards their goals throughout the game (even if in actuality there are losing pretty badly). New players wouldn't even realize they are losing, really, and still have a sense of accomplishment at the end of the game regardless! The board is attractive, the pieces have a nice tactile sense, and the game overall has a theme that feels really integrated and natural rather than slapped on and made-up. Both young and old alike can play very successfully, and it gives a good sense of the geography of the United States as well.
Settlers is the first euro-style board game that I ever played. Rules were pretty easy to pickup. Definitely has some element of luck since you are subject to random chance of which spaces are available to you at the beginning of the game as well as the roll of the dice during each turn. One unique thing is that psychology and group dynamics can have large affects through the ability to trade resources. Winning strategies mitigate the feast and famine of the rolls of the dice by diversifying the dice rolls that yield resources. It isn't my favorite board game probably because I lose at a greater rate than other games. I also hate it when the robber gets put on resources I am connected to and can't reap a harvest. It's best for my enjoyment to play games where other players can't actively "hurt" me :)