A Game of Thrones:
http://www.amazon.com/Game-Thrones-The-Board-Second-Edition/dp/1589947207
For regular players, it is just a really good strategy game. For fans of the source material, it doubles in very carefully recreating the war of the five kings, with accurate geography and various characters from the books appearing as generals and leaders. The balance is great, every turn is tense, diplomacy is vital and backstabbing (eventually) neccesary. You get battles on land and sea, manage resources, deal with harsh conditions and possible wildling raids. Even things like the strenght of your claim on the throne, your standing in the court and the prowess of your armies are represented and influence how your game turns out. And, in my opinion the absolulte must have selling point,
nothing in the game comes down to luck. (you can add "battle luck" cards if you wish, but I strongly advise against that). It all comes down to your planning, your anticipation of what other players do and your skill at manipulating them. Even though the starting positions are always the same, games tend to turn out drastically different each time.
So, if you want the experience of leading one of the six great houses to victory in Westeros, this is your game. Or if you like ASOIAF. Or strategy games. Or having fun. :3
The only downside is that you really need to get six motivated people to play with you for an approx. 2 - 4 hours. Organizing such a group isn´t always easy. Sure, you can play with fewer people, but the balance won´t be nearly as good and the excitement of everyone being surrounded by rivals will be missing. For the game to reach its full potential, having six players is required.
The other big board game I play is Arkham Horror.
http://www.amazon.com/Fantasy-Flight-Games-VA09-Arkham/dp/1589942108
It is cooperative game, so thankfully a good change of pace when compared to the tense PvP of Game of Thrones. The players take the roles of investigators in the 1920s town of Arkham which is swarmed by Lovecraftian evil. The players need to gather clues and equipment to fight off various monsters on their way, venture through tears in the dimensions and seal the portal before the Ancient One awakes.
This game plays much more like a RPG and puts heavy focus on telling dramatic stories rather than giving the player control over what happens. There are tons of player characters with various abilities, tons of equipment, tons of encounters to be had various dimensions to travel through, a lot of monster, different ancient ones which inluence the board in different ways and all have their own unique final battle (which you have to face if you fail to stop its awakening). The replayability is enormous and the various tales you will create with your playthrough will stick with you long after the game has ended. Like that one time where a very dangerous monster showed up in a suburp, but none of our characters was strong enough to defeat it. Luckily, we got our hands on a time bomb and sent one guy on a suicide mission, but the random event on the trainstation had him take the wrong train and fall into another dimension... or the one time where a neighborhood was swarmed with beasts, blocking our progression, when suddenly the gangs of that area swarmed from their hideouts and beat the monsters back with pipes and shivs... and so on.
What I really like about this game is that, if you play it properly, it is really hard. Success rate can be below 1/3rd and constant doom is always hanging above you. No matter where you are and what you do, you will always feel underpowered and various "Oh Crap" moments will happen. Always hoping for that lucky roll so you can hang on, but always curious what other horrors the game has to throw at you... and infinitely satisfying when, against all odds, you *do* manage to succeed and banish the Ancient One... for now.
